"If a child is not in school, they stand to lose far more than just a few months of learning. It could well put a huge dent in their future life chances," Mr Williamson said in his open letter to parents.
"Education is a birthright, so let's make sure we get all children back - back to learning, back to playing and back to being kids again."
Mr Williamson said it was "generally accepted" that children's health and wellbeing is more at risk if they do not go to school.
He cited a joint statement by the UK's chief medical officers, which said "very few, if any" children and teenagers would come to long-term harm from Covid-19 solely by attending school.
The letter was published just as the government faced criticism for the timing of its guidance sent to schools in England, just days before most children begin term.
The guidance said that, in local lockdowns, secondary pupils could be kept home every other fortnight and, in an outbreak, large groups could be told to self-isolate.
While not addressing the teachers' criticism in his open letter, Mr Williamson reassured parents that the health risk posed to children by Covid-19 is "extremely low".
He said "huge lengths" had been taken to prepare schools for pupils' return, including children being placed in groups - or "bubbles" and the wearing of face coverings in communal areas of schools under lockdown.
He said the "priority" was for children to return. "It really is the best place for them to be," he added.
Schools in Scotland and Northern Ireland have already been allowed to reopen.
Universities in the UK are being urged to scrap plans for face-to-face teaching until Christmas in order to prevent a second wave of coronavirus.
Academics' union, UCU, said more than a million students moving around the country was "a recipe for disaster".
UCU leader Jo Grady said universities were not prepared, and risked becoming the "care homes of the second wave".
But university bosses say they have worked hard to plan for a safe return to all aspects of student life.
When the students return in September, they will be expected to abide by new policies on the use of face coverings and social distancing protocols.
Meanwhile there will be safety partitions to keep them apart, as well as more cleaning and ventilation and smaller class sizes where face-to-face teaching takes place.
When national lockdown measures were brought in at the end of March, universities cancelled lectures, tutorials and some exams. Many continued their lessons and lectures online however, and even held final exams remotely.
Over the summer, universities have been preparing for the return of their students' return, with most promising a mix of face-to-face and online learning - or "blended learning" - with students learning in extended "bubble" groups.
But few, if any, universities have taken the step of telling their students not to move into their accommodation.
Ms Grady said having tens of thousands of students heading into cities across the UK "risks doing untold damage to people's health and exacerbating the worst public health crisis of our lifetimes".
She said: "We are very concerned that universities, and the UK more generally, are simply not prepared for the mass migration of what is over a million students.
"In particular, we are concerned about students going from high risk areas into areas with fewer cases."
She said she was particularly worried about the risk of the virus spreading in cities with big student populations.
"Mrs Grady said: "If we look at some key cities: Manchester has 100,000 students; Birmingham isn't far behind with 80,000; and Leicester has 40,000.
"These are all cities that have had some form of local lockdown and have come out of it or are about to go into one."
She added: "We don't have a functioning track and trace [system], we don't have a UK-wide testing for students who are arriving for university, or subsequent and regular testing.
"We are really worried about young people congregating in halls of residence and just what this will mean in terms of transmission.
"We don't think sufficient safety measures are in place," she added.
The union said it was backing the position of the Independent Sage committee which has called for online learning to be universities' default position.
The already difficult situation, with universities doing their best to bring in socially distanced ways of working, has been made worse by the higher than expected number of students this year, she said.
'No regular testing'
The exams crisis over the summer meant many more students ultimately achieved the grades needed to get into university, after the government's last-minute change of mind on school-assessed grades.
The UCU says there will be challenges in ditching the blended learning approach, and replacing it with online-only teaching.
But Ms Grady said it was time for the government "to finally take some decisive and responsible action in this crisis and tell universities to abandon face-to-face teaching".
She also called on the government to underwrite any loss of fee income to universities, and to support students who have problems in connecting remotely.
National Union of Students president Larissa Kennedy said universities should only deliver face-to-face teaching for lab-based and practice-based courses.
"In-person teaching should only take place if can be delivered safely for all staff and students, and social distancing guidelines and other safety measures can be maintained," she said.
She backed calls for more student support with remote learning and urged universities to work with their student unions on decisions about how best to re-open campuses.
Universities UK president Julia Buckingham said: "Many staff want to return to in-person teaching, research and other activities where it is safe and appropriate to do so."
They are also mindful of the benefits of in-person teaching and support for students' well-being and development, he said.
"The dedication shown throughout the lockdown and into recovery has been remarkable," she added.
'Constant review'
A Department for Education spokesman said: "We are confident that universities are well prepared for the return of students by taking measures such as introducing social distancing on campus, limiting travel requirement for classes and staggering teaching across extended days to reduce numbers on site.
"Opening universities is a part of the Prime Minister's cautious roadmap, and it is important that we continue to open education settings wherever it is safe to do so.
"We support face to face teaching only where possible and if safety guidelines are followed, but know that high quality online teaching can also be delivered if necessary.
"We are keeping our guidance under constant review, and are currently updating our advice on reopening higher education buildings and campuses to reflect the latest public health advice, including on face coverings, local lockdowns and test and trace."
Universities could become the "care homes of the second wave of COVID-19", a higher education union has warned.
In an exclusive television interview with Sky News, The University and College Union (UCU) says the government and universities are risking public health by pushing on with plans to fully reopen campuses in a few weeks' time.
The start of a new university year is "the biggest migration of people on an annual basis in the UK," Jo Grady, UCU general secretary, says.
"That's a million students, moving across country, cycling in and out of lockdown zones, of bubbles, of homes, into new cities, where we are not track and tracking those students, we are not testing those students," she said.
"We are seriously concerned that if the government and universities do not step in and discourage this...we could see universities becoming the care homes of the second wave of COVID-19."
Advertisement
The UCU wants, at the very least, for the government to enforce mandatory COVID-19 testing of students on arrival.
But some staff who work in universities believe that student numbers should be restricted altogether.
More from Covid-19
"It's not worth the risks of coming in for face-to-face teaching," university research fellow Eric Lybeck told Sky News.
"There are some exceptions I can see where lab facilities are needed, or disadvantaged students might not have access to the internet or certain health concerns where perhaps some access to university facilities could be provided.
"But wherever young people can do their seminars, small group teaching, lectures online it just seems that that is the right thing to do until the government gets a handle on the pandemic."
Image:University research fellow Eric Lybeck warns face-to-face teaching is 'not worth the risk'
Following the changes to the A-Level results, many universities reported having to accept more students than they had initially accounted for, complicating existing social distancing plans.
The UCU says the government should financially back institutions that "do the right thing by public health" and move services online, so that they avoid loss of income through missed tuition and accommodation fees.
It has been a torrid summer for this year's cohort of freshers, who have had exams cancelled, grades remarked and university places awarded and taken away.
James Appiah, 18, who is set to start at the University of Cambridge next month, said restrictions on joining his classmates would "ruin the expectation I have of going to Cambridge".
He added: "I expect to see my lecturers face-to-face, go and have a good time with my friends, to network with people.
"Online learning is not exactly a big loss, I believe it'll only be for the first year, as long as there is not a second wave of the coronavirus, but [if I stayed at home] I'd be very upset about it."
Image:James Appiah says he would be disappointed if pupil numbers are restricted at Cambridge
The Department of Education says that "we are confident that universities are well-prepared for the return of students."
"The safety and well-being of university staff and students is always our priority.
"We are keeping our guidance under constant review, and are currently updating our advice... including on face coverings."
Business leaders rage at Matt Hancock's 'scaremongering' talk about a second lockdown as they warn of 'untold damage' to businesses trying to recover from coronavirus lockdown
Business leaders responded with shock and disbelief to Mr Hancock's comments
He said that England could face restrictions and very extensive local lockdowns
He also warned he warned other countries were experiencing a second wave
Health Secretary Matt Hancock has been slammed for ‘scaremongering’ talk about a second lockdown that risks ‘untold damage’ to businesses trying to recover from the first one.
The under-fire Minister told The Times yesterday that England could face nationwide restrictions and very extensive local lockdowns in the event of a second wave of Covid-19 this winter.
In an interview he warned countries in others parts of the world were already experiencing a second wave and claimed it was ‘a very serious threat’.
Mr Hancock also hinted that if a vaccine is not ready soon, grandparents would be unable to hug their grandchildren this Christmas.
Mr Hancock (pictured) also hinted that if a vaccine is not ready soon, grandparents would be unable to hug their grandchildren this Christmas
Last night business leaders responded with shock and disbelief at the timing and the tone of Mr Hancock’s comments.
They come just days before children are set to return to schools in England and ahead of a major Government advertising campaign to encourage workers back to their offices.
Leading City financier Dame Helena Morrissey told The Mail on Sunday: ‘I find it very frustrating – it’s incredibly inconsistent.
‘I’m really not sure at this stage that the country needs more scaremongering. And I find it very perplexing and very disappointing that he’s putting fear in.
'Just as children are getting ready to get back to school, this talk of a second wave is very dangerous.
'I think that Matt Hancock seems to be marching to his own tune.
‘He seems to be saying things that don’t fit at all with some of the other advice that we’re being given and obviously I think the balance of risks has shifted from all health to health and the economy.’
Charlie Mullins, founder of London firm Pimlico Plumbers, said: ‘How long can we carry on like this?
'I don’t think he’s helping and I feel that he needs to be more encouraging than discouraging.
'If we don’t go back to work, we’re all going to be worse off anyhow because obviously there won’t be jobs to go to.
Mr Hancock also faced a backlash online, with travel industry expert David Speakman lambasting the Health Secretary on Twitter: ‘Loose talk by Matt Hancock doing untold damage to business unable to plan by irrational government policy’ and asked ‘Where is Boris Johnson [and] Michael Gove putting him in line?’
He added: ‘It illustrates the disconnect between the people and the Establishment. The Establishment that believe they know better and try to rule rather than support… Career politicians don’t help.’
Clive Jacobs, founder of leisure car hire firm Holiday Autos, agreed: ‘When history is written in years to come people will laugh at how imbeciles like him were allowed to destroy our way of life unnecessarily.’
It came as Covid-19 infections fell 14 per cent on last week’s figures, with 1,108 people testing positive in the 24 hours up to yesterday.
In the same period, the UK recorded 12 deaths to bring the tally to 41,498.
The total number of cases has risen to 332,752, and there is now an average of 1,173 new cases each day.
More than 1,000 positive tests have been confirmed on 16 days this month, after a run of no four-figure days throughout June and July.
The Italian coastguard has helped a rescue boat funded by British street artist Banksy after the vessel became stranded in the Mediterranean Sea.
The boat was unable to move due to an overcrowded deck after picking up 219 migrants off the Libyan coast since Thursday.
The crew said on Twitter they were close to declaring "a state of emergency" as the already-crowded ship had lent assistance to a boat with 130 migrants and a dead body onboard.
The crew claimed European officials ignored repeated calls for help - but the Italian coastguard has since told Sky News that one of its ships has taken on board 49 "of the most vulnerable" refugees, include 32 women, 13 children and four men.
Used to help migrants in the Mediterranean trying to reach Europe from North Africa, the 31-metre-long motor yacht, which is a former French navy boat, features some of Banksy's trademark work, including a girl in a life vest holding a heart-shaped safety buoy.
Advertisement
Image:Banksy funded the boat built to rescue migrants in the Mediterranean
The artist reportedly asked former captain of several NGO rescue boats, Pia Klemp, to use his money to fund "a new boat," which was named Louise Michel after a 19th-century female French anarchist and teacher.
On Friday morning, the crew posted on the boat's official Twitter page that they had rescued 89 people, including 14 women and four children, and were seeking a place of safety for them to disembark.
More from Migrant Crisis
That evening, it said it lent assistance to another overcrowded boat, which was filling with water, had a dead body on board and many more suffering fuel burns.
"Louise Michel just responded to a mayday relay by #Moonbird aircraft for a rubber boat in distress that had no movement & was taking in water," the tweet read.
"Louise Michel proceeded at full possible speed & handed out life vests to 130 people to secure the situation. Authorities, your turn."
The crew said they put emergency calls out to agencies from Germany, Malta and Italy but were ignored.
They wrote on Twitter on Saturday: "#LouiseMichel is unable to move, she is no longer the master of her manoeuver, due to her overcrowded deck and a liferaft deployed at her side, but above all due to Europe ignoring our emergency calls for immediate assistance."
"We repeat, #LouiseMichel is unable to safely move and nobody is coming to our aid. The people rescued have experienced extreme trauma, it's time for them to be brought to a #PlaceOfSafety. We need immediate assistance".
The crew posted a video of the overcrowded boat, writing: "These are the survivors you are turning your back on #EU. After escaping untold horror and inhumanity they need a place of safety."
🔴Alert! #LouiseMichel assisted another 130 people - among them many women & children - and nobody is helping! We are reaching a State of Emergency. We need immediate assistance, @guardiacostiera & @Armed_Forces_MT. We are safeguarding 219 people with a crew of 10. Act #EU, now!
A crew of 10 European activists are on the ship, which last week left Burriana in Spain and had sailed to an area about 90 miles southeast of the Italian island of Lampedusa.
Banksy posted a promotional video on his official Instagram page, with the words "Like most people who make it in the art world, I bought a yacht to cruise the Med" overlaid with pictures of Louise Michel and migrants in distress.
"It's a French navy vessel we converted into a lifeboat because EU authorities deliberately ignore distress calls from 'non-Europeans'," the video continued.
The ship's launch on 18 August was kept secret and news of the mission has only been released following its first rescue.
While it is fairly small, the yacht has a top speed of 27 knots and so is considerably faster than other NGO rescue vessels.
The crew managed to keep #LouiseMichel stable for almost 12h now. Our new friends told us they lost 3 friends on their journey already. Including the dead body in our one life raft, that makes 4 lives vanished because of Fortress Europe... And we are still waiting. pic.twitter.com/Te2PKCv2Gn
On Wednesday, 45 people - including five children - died when the engine on their boat exploded off Libya, in the country's deadliest shipwreck this year.
Over 7,600 migrants have been discovered at sea and returned to Libya so far this year, according to figures from the International Organisation for Migration.
Head teachers and teachers have criticised the government for "last-minute" guidance on what to do during virus outbreaks and local lockdowns.
The guidance for England was published on Friday evening, just days before many schools begin term.
The NAHT school leaders' union said the timing was "reprehensible".
In local lockdowns, secondary pupils could be kept home every other fortnight and, in an outbreak, large groups could be told to self-isolate.
Paul Whiteman, general secretary of the NAHT, said the decision to publish the guidance on a Friday evening before a bank holiday was "nothing short of reprehensible and demonstrates a complete lack of regard for the well-being of school leaders and their teams".
He said: "It was obvious weeks ago that lockdown advice was necessary."
In areas where additional coronavirus restrictions have been introduced because of rising cases, secondary schools have been told they might have to limit the number of students and bring in a rota system, with each pupil spending a fortnight at school then a fortnight learning remotely so as to break the chain of Covid-19 transmission.
The guidance says this would only happen after "all other measures have been exhausted" - but that if cases continued to increase, all students might have to move to remote learning apart from those in vulnerable groups or whose parents were key workers.
Education Secretary Gavin Williamson said the document was a contingency plan for a "worst-case scenario", which he hoped would not need to be implemented.
How schools will respond to local lockdowns
There are four stages of response, depending on the level of virus cases in the area:
Tier 1: All pupils attend as normal.
Tier 2: Secondary schools and colleges move to rotas, with students alternating a fortnight attending and a fortnight at home. Primary schools remain open to all.
Tier 3: Most secondary pupils learn from home as secondary schools and colleges are only open to vulnerable children, the children of key workers and selected year groups.
Tier 4: All schools switch to remote learning, except for vulnerable children and the children of key workers, and students at alternative provision and special schools.
The guidance also sets out what to do when a school confirms a case of coronavirus. Health protection teams will advise the school how many pupils need to be sent home to isolate for 14 days.
If a case occurs where the "bubbles" used to limit pupils' contacts in schools are smaller, such as a single class, all those in the bubble might have to be sent home to isolate.
In bigger bubbles, such as an entire year group, health protection teams could send home all the other pupils, or limit self-isolation to those who were in direct contact or close proximity or who had travelled with a pupil with the virus.
Patrick Roach, of teachers' union NASUWT, said the government needed to give schools the resources to cope with the potential disruption, including support for remote learning and cover for staff absence due to self-isolation.
"The availability of staff where there is a local lockdown or outbreak may mean that schools have to limit provision if they cannot be staffed safely," he added.
Geoff Barton, leader of the ASCL head teachers' union, said he felt a "weary, resigned sense of inevitability" to receive the guidance at the last minute, after head teachers had been accused of "treachery" for asking for contingency planning for outbreaks.
He said more needed to be done to support students in exam years who might find their teaching disrupted, including ensuring they had access to laptops to study at home.
"We have to do better than previously," he said. "We simply cannot have those young people being left at home without clear guidance on what they're going to do."
Mary Bousted, joint general-secretary of the National Education Union, said the guidance should have been ready "months ago".
Labour's shadow education secretary Kate Green told Sky News the guidelines were "long overdue" and it was "unfair" to school and college leaders to release them so close to the start of term.
The guidelines on introducing rotas only apply to secondary schools. Prof Neil Ferguson, a former advisor to the government on the pandemic, told BBC Radio 4's Today programme primary schools often only had "the odd case" without evidence of wider transmission, so there was less need for the measures.
But he said schools also needed "very rapid testing" of students and staff to control outbreaks.
Prof Carl Heneghan, a Oxford University epidemiologist and practising GP, said cold and flu cases meant many pupils would have to self-isolate until they could be tested, so schools and families faced "significant disruption".
"If your child has any symptoms they're going to have to stay off school. In the past there's been a tendency to say, you can have some Calpol, maybe you can go in. But there's going to have to be a sea-change in how parents behave with their children," he said.
Analysis: 'Remote learning will still be a reality'
By Dan Johnson, BBC News
Head teachers had asked for a Plan B and here it is - but there's frustration it came just days before more children are due back in the classroom across England.
A suggestion of entire year groups or classes - "bubbles" - having to automatically self-isolate was deleted, but not before it added confusion.
The Department for Education is now pointing to more nuanced guidance about head teachers and public health officials needing to establish who's been in "close contact" with anyone who tests positive.
There's recognition that schools won't be immune from outbreaks in local communities and, while the intention will be to stay open and keep children in class, there's an acknowledgement that further interruptions to learning are possible.
Primary school pupils are the clear priority. Secondary schools will first adopt a rota system before more prolonged disruption, meaning remote learning will still be a reality for some children.
Meanwhile, Health Secretary Matt Hancock has not ruled out nationwide restrictions should England see a spike in coronavirus cases this winter.
He told The Times a second wave was "a very serious threat" and that, under a "reasonable worst-case scenario", Britain could be faced with a spike in Covid-19 cases and a bad outbreak of seasonal flu as people spent more time indoors.
In other developments:
A leaked government report suggests a "reasonable worst-case scenario" for the UK this winter is 85,000 deaths due to Covid-19, with more restrictions reintroduced but schools remaining open
Hundreds of people in Trafalgar Square demonstrated against the UK government's coronavirus measures, holding banners with slogans such as "Covid hoax"; similar protests have taken place in Berlin and Paris
There could be nationwide restrictions or very extensive local lockdowns in England if there is a second spike in COVID-19 cases this winter, Matt Hancock has warned.
The health secretary also said in a worst-case scenario, the UK could be fighting a bad outbreak of flu and a growth in coronavirus as people spend more time indoors.
He said: "Cases go up again, and we have to use very extensive local lockdowns or take further national action. We don't rule that out, but we don't want to see it."
Govt issues 'levels of urgency' for schools in lockdown
Mr Hancock claimed social-distancing measures would remain for the "foreseeable" future and suggested that, unless a vaccine was approved, grandparents would be unable to hug their grandchildren this Christmas.
"I yearn to be able to remove the restrictions on social contact but those restrictions are absolutely necessary at the moment.
Advertisement
"We'll be keeping them in place for the foreseeable. We hope for the best and we prepare for the worst."
Speaking to The Times, Mr Hancock said a second wave could be "avoidable but it's not easy", with schools reopening next week presenting new challenges in stopping the spread of the virus.
More from Covid-19
He said countries in other parts of the world were already experiencing a second spike, adding it was "a very serious threat".
But he said the UK was managing to keep the number of new cases "flat" through the test and trace system and local lockdowns.
Workers in Europe 'keen to return to office'
Under the initial lockdown in March, retail and hospitality industries had to close across the country.
Boris Johnson has compared the prospect of another nationwide lockdown to a "nuclear deterrent".
The health secretary said a vaccine was likely to be available "some time next year", although he hoped this would be sooner.
Before then, he said, the government was relying on three "lines of defence" to stop the spread of coronavirus - social distancing, NHS test and trace, and local lockdowns.
He hoped these measures, combined with the biggest flu vaccination programme in history, would ensure that the NHS could cope.
'Weary inevitability' about govt guidance on schools
His comments come as local COVID-19 restrictions were eased in northern England, which will allow social gatherings between two homes from Wednesday in Bolton, Stockport, Trafford, Burnley, Hyndburn and parts of Bradford, Calderdale and Kirklees.
Meanwhile, the latest R number range for the UK remains the same as last week at 0.9-1.1 - indicating the rate of infection is most likely either broadly stable or slightly growing.
The R number is a measure of how many people on average each infected person transmits the virus to.
The latest growth rate for the whole of the country is between -2% and 1%, the government said, meaning the number of new infections is somewhere between shrinking by 2% and growing by 1% every day.
Official government data released on Friday revealed the UK recorded 1,276 daily confirmed cases of COVID-19, compared with 1,522 a day earlier.
