Boris Johnson has suggested Parliament could move to York while the Palace of Westminster undergoes renovation.
In a letter, the prime minister said the government was considering establishing a hub in the northern city and "it would therefore make sense to consider this as a potential location".
The move, if it happens, is expected to take place around 2025.
Other possible London locations proposed by Mr Johnson in the letter to David Goldstone and Sarah Johnson, who are overseeing the restoration project, include Richmond House, the QUII (Queen Elizabeth II Centre) and City Hall.
Mr Johnson said that the case for both Houses staying in place should also be considered.
In his letter, seen by the BBC, the prime minister said: "We all have a responsibility to protect the Palace of Westminster as a functioning building and as the iconic UNESCO World Heritage site that is the home and symbol of our democracy.
"The current situation is unsustainable given the serious risk of a major fire and the need to upgrade the services throughout the building."
Mr Johnson added that "costs are obviously a major driver" in the review but said other factors including disruption to Parliament's work, the timelines for delivery, heritage benefits and fire safety, should be considered.
"We should also move as quickly as possible, both because of the risks associated with the current state of the building and the need to provide certainty on the way forward and thereby minimise disruption to our business," he added.
The letter also said that the location of Parliament was a constitutional issue and that the views of parliamentarians would need to be considered carefully.
The review into the project and the potential move is expected to report its recommendations in the autumn.
Before Parliament voted in 2018 to approve the renewal works, which would entail decanting the whole building for at least six years, MPs had pushed rival plans that would have seen only a partial vacating required. This would have forced builders to work around the Commons schedule.
A recent report by the National Audit Office (NAO) stated that the £4bn cost previously reported for the restoration project was likely to be a "median" figure, with the final outlay expected to be higher.
When the nine members of the powerful Intelligence and Security Committee (ISC) of parliament filed into the Macmillan Room of Portcullis House at 5pm for the first meeting of the new committee, Chris Grayling thought he had the chairmanship in the bag.
After all, the former cabinet minister and Brexiteer was Boris Johnson's choice - controversially, given his record in government and lack of expertise on intelligence and security - and he had already nominated himself the day before.
Nothing could go wrong, he must have thought, because the Tories had a five-four majority on the nine-member committee.
But Mr Grayling and the government whips had both made a major blunder. Neither had sounded out the senior Tory backbencher Dr Julian Lewis and made sure that he was going to vote for Mr Grayling.
And when the committee clerk asked at the start of the meeting if there were any more nominations for chairman, Dr Lewis nominated himself and was immediately backed by the three Labour and one Scottish National Party member.
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Result: 5-4 to Dr Lewis, leaving Mr Grayling - cruelly lampooned as "failing Grayling" after his accident-prone cabinet career - and the prime minister humiliated, and the Number 10 machine who were so desperate to see their loyalist nomination elected absolutely furious.
"Grayling is the only person ever to have lost a rigged election," said one Tory MP.
More from Boris Johnson
Mr Grayling had been ambushed. It had been a bloodless coup. But that was about to change.
Within an hour of the decisive vote in the Macmillan Room, it emerged that the committee would meet again at 10am the following morning and almost certainly agree to publish the committee's long-suppressed report on allegations of Russian meddling in UK politics.
Image:Chris Grayling had been expected to become the new ISC chair
But a crisis for the prime minister was then immediately turned into a drama by Number 10, when Dr Lewis was informed by the government's burly bruiser of a Chief Whip, Mark Spencer, that he had been kicked out of the Tory parliamentary party.
Dr Lewis had the whip withdrawn, government sources told Sky News, "for working with Labour and other opposition MPs for his own advantage".
Another source said: "There are consequences for that duplicity."
The decision sent shockwaves through Westminster.
"This is gangster politics," one member of the committee was reported to have said.
The consensus among many MPs was that Number 10 was guilty of a massive overreaction which has made what was only a moderately bad situation much, much worse.
Dr Lewis has suffered the fate of the 21 pro-Remain Tory MPs who defied Mr Johnson in Brexit votes last year, including - in a delicious irony - the former chairman of the ISC, Dominic Grieve.
Image:Julian Lewis MP, pictured in 2005
One senior MP told Sky News: "This would have blown over in a few days. Now there will be a huge row throughout the weekend and into next week.
"Removing the whip from Julian also massively strengthens his authority and boosts his independence from the government.
"He is also very popular with the Tory old guard on the back benches, the old knights of the shires, the Thatcherites and the veteran Brexiteers. He's one of them and they won't like it."
Dr Lewis is indeed popular with MPs on both sides of the House.
He was a successful chairman of the Defence Select Committee for four years. He is independent-minded and, despite being a Brexiteer, was a big defender of John Bercow during the former speaker's battles with Mr Johnson last year.
MPs blame the prime minister's controversial adviser, Dominic Cummings, for Number 10's brutal revenge on Dr Lewis.
"This isn't the Chief Whip's decision," one senior MP told Sky News.
"It's Cummings. And it's absolutely bonkers."
Number 10's retribution against Dr Lewis may not be over, however.
The rules governing the ISC, in the Justice and Security Act of 2013, state that the chairman is elected for the whole parliament, until the next election.
But there is already talk of the government tabling a Committee of Selection motion, which can be debated for up to 90 minutes and then voted on by MPs, removing Dr Lewis from the committee and replacing him with another Tory MP.
That would cause a huge row. But would the PM, in his current belligerent mood, care?
And in the chamber, of course, Mr Johnson has a majority of 80. Well, he did. It's down to 78 now, with Dr Lewis presumably crossing the floor to sit with the opposition.
One MP even suggested the PM could go for the nuclear option of abolishing the Intelligence and Security Committee altogether.
Out of the question? Probably not while Mr Cummings is advising Mr Johnson.
Despite his humiliation, Mr Grayling remains a member of the committee and could yet - theoretically - still become chairman if Dr Lewis is kicked of the committee and replaced by a Johnson loyalist.
Besides Mr Grayling, the other outvoted Tories are another ex-cabinet minister Theresa Villiers, ex-minister Sir John Hayes and backbencher Mark Pritchard.
It was Labour MPs Dame Diane Johnson and Kevan Jones, Labour peer Lord West and SNP MP Steward Hosie who backed Dr Lewis.
When Dr Lewis walked into the Macmillan Room in Portcullis House at 5pm, he obviously knew he had the support of the opposition MPs on the committee.
But with Boris Johnson in vengeful mood, he may need the support of many other Tory MPs if he is to survive this fight to the death with the prime minister.
THE Tories were plunged into civil war last night as Boris Johnson sacked a senior MP for colluding with Labour and the SNP to get a top job.
Julian Lewis was booted out after he humiliated the Prime Minister by working with rivals to gazump his pick for chair of the intelligence and security committee.
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MP Julian Lewis has been booted out of the Conservative PartyCredit: PA:Press Association
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Chris Grayling is said to have had the backing of Boris Johnson to take the Chair's roleCredit: PA:Press Association
No 10 had chosen ex-Cabinet minister Chris Grayling for the role and expected all Conservative MPs to back him.
But the former justice and transport secretary was a controversial choice due to his poor record in numerous top government jobs.
Dr Lewis was appointed to the powerful job at the last moment after gaining the support of all four Labour and SNP members of the committee.
It is now expected to meet today and agree to publish a long-awaited report into Russian meddling in UK politics as early as next week.
A government source Dr Lewis had been stripped of the whip “because he worked with Labour and other opposition MPs for his own advantage”.
The committee oversees the work of MI5, MI6 and GCHQ, and there had been concern about Mr Grayling’s expertise for the chairmanship.
He worked with Labour and other opposition MPs for his own advantage
Government source
Former national security adviser Lord Ricketts had warned that Mr Grayling - who earned the nickname “Failing Grayling” during a chequered ministerial career - does not “match up” to the authority and reputation of former chairs.
Following Dr Lewis’ success, Lord Ricketts said the body was now in the “hands of someone with much wider experience of defence and security”.
As well as Mr Grayling and Dr Lewis, the members of the ISC are Tory MPs Theresa Villiers, Sir John Hayes and Mark Pritchard, Labour MPs Dame Diana Johnson and Kevan Jones, the Labour peer Admiral Lord West and the SNP MP Stewart Hosie.
Mr Johnson has faced criticism over the delay in appointing the committee which has not met since the last parliament was dissolved in November last year.
The committee has yet to publish its long-awaited report into Russian interference in UK politics after Mr Johnson refused to clear it for release before last year’s general election.
A committee source told the PA news agency: “This was a secret ballot but clearly for him (Mr Grayling) to lose, some Tories decided not to vote for him.”
'GRUBBY'
Labour's deputy leader Angela Rayner branded the move against Dr Lewis "grubby".
She tweeted: "Julian Lewis MP has the Tory Whip removed after being elected as Chairman of the Intelligence and Security Select Committee, after beating hapless Chris Grayling.
"I wonder who in No10 ordered that the long serving Tory MP had the whip removed? What a grubby shower they are!"
Labour former frontbencher Chris Bryant said: "It's a momentous failure of intelligence when a PM takes months to handpick Intelligence and Security Committee members so as to deliver the Chair he wants and they refuse to do his bidding.
"To then chuck the new chairman out of the party is to lose control/the plot."
SNP defence spokesman Stewart McDonald MP said: "This is another total shambles from the Tory government, which has failed to put in place a functioning Intelligence and Security Committee for more than six months since the election.
"With his abysmal record of failure as a Tory minister, Chris Grayling is the only man who could lose a rigged election but it is right the committee has elected a chair and it should now get on with the crucial job of ensuring scrutiny and oversight of security matters, after months of delay."
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Liberal Democrat foreign affairs spokesman Alistair Carmichael said Mr Johnson had appointed "yes men" to the ISC but "true to form, however, failing Grayling has been undone in his bid to be chair".
"I hope we now have a committee with real teeth that can hold this Government to account," he added.
"That starts by publishing the report into Russian interference of our democracy before the summer recess so MPs can scrutinise it fully."
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The Conservatives have removed the whip from Julian Lewis, effectively booting him out of the party
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Chris Grayling had been Boris Johnson's preferred choice for the committee chair roleCredit: Getty Images - Getty
SNP Westminster leader Ian Blackford has been branded 'extremely rude' after refusing to sit down during a fiery Commons Brexit debate.
Blackford intervened on his colleague Pete Wishart to raise concerns on the government's approach to devolution on Brexit matters.
But his speech was far longer than MPs expected, prompting the deputy speaker to interrupt.
Dame Rosie Winterton said: "It's quite a long intervention."
She calledWishart to resume his speech, but Blackford continued speaking - prompting a furious response from the Tory benches while Dame Rosie urged him to stop.
Blackford thundered: "I will say to the Deputy Speaker, that Scotland's voice will be heard."
Dame Rosie replied: "That was extremely rude, extremely rude, extremely rude. The honourable gentleman must resume his seat."
Shouts of "sit down" could be heard from the Tory benches among other heckles.
Wishart said Blackford was right to be "absolutely furious" about Westminster's plans for Scotland.
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He said of the Tory MPs: "They're all bawling and screaming, put the cameras round on them.
"We want Scotland to see you screaming at us, that builds support for us, keep on doing it."
Wishart said Scotland is "making up its mind" on its future, adding: "Scotland will become an independent nation in the next year.
In a statement, it said: "We need to know that any inquiry will be public with the ability for families to contribute their experiences and that it will have the power to access all of the evidence and witnesses needed.
'Disappointing'
"We also believe that a part of any inquiry must begin now to take fast action in order to prevent further unnecessary deaths should we encounter a second wave."
The group added that it was "so disappointing the prime minister is refusing to meet with or listen to bereaved families".
At Prime Minister's Questions, acting Lib Dem leader Sir Ed Davey said the UK had "suffered one of the worst death rates in the world and Europe's worst death rate for health and care workers".
If the PM "still rejects an immediate inquiry," he asked, "will he instead commit in principle to a future public inquiry?"
Mr Johnson said now was not the "right moment to devote huge amounts of official time to an inquiry".
'Real teeth'
But he added: "Of course we will seek to learn the lessons of this pandemic in the future and certainly we will have an independent inquiry into what happened."
Downing Street was unable to give any further details about the nature of the inquiry when pressed on whether it will be judge-led or when it will begin, saying that the remit would be set out "in due course".
Sir Ed Davey said he had written to the prime minister to ask him to "confirm that it should be an inquiry under the Inquiries Act 2005," which he said would give it "real teeth… to get to the bottom of the issue".
He told BBC news he had called for an inquiry "because there's been tens of thousands of deaths" and the bereaved families "need to have some answers". He also said an inquiry should look at the economic impact of the virus.
This is quite a significant moment.
We know from past inquiries, like the Iraq inquiry or the Leveson inquiry into the media, that they can shape the reputations of the most powerful and probe their innermost thinking in moments of crisis in a way that's often hard to do through the normal scrutiny of politicians and journalists.
But there are an awful lot of unanswered questions.
We don't really know what the prime minister meant when he talked about an independent inquiry - that could be a full blown judge-led inquiry or a much lower calibre investigation led by an academic or maybe a select committee.
We don't know the timeframe. The prime minister has indicated he does not think we should hold the inquiry while we're still grappling with coronavirus but that means it could be months, even years away.
We don't know the remit of the inquiry or the authority - will it be the sort of inquiry where witnesses are questioned under oath by barristers led by a judge?
My guess, and it is only a guess, is that it will have to be of similar stature and authority to the Iraq inquiry.
Sir Ed's rival for the Lib Dem leadership, Layla Moran, who chairs an all-party group on coronavirus, called on the prime minister to "commit to a public inquiry now, not kick this into long grass".
'Aware of report'
During PMQs, Labour leader Sir Keir Starmer pressed the prime minister on whether he had learned the lessons of a report this week, which warned about 120,000 new coronavirus deaths in a second wave of infections this winter.
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"One of the key recommendations in this report commissioned by the government's office for science, is that testing and tracing capacity will need to be significantly expanded to cope with increased demands over the winter," said Sir Keir
"The reality is this - trace and track is not working as promised as it stands today."
The Labour leader questioned whether the prime minister had even read the scientists' report.
Mr Johnson said he was "aware of the report" but accused the Labour leader of "endlessly knocking the confidence of the people in this country" with criticism of the government's approach.
He added: "Our test and trace system is as good as or better than any other system in the world and yes, it will play a vital part in ensuring that we do not have a second spike this winter."
'Kidding no-one'
Sir Keir said it was "perfectly possible to support track and trace and point out the problems".
He told the PM that "standing up every week and saying it's a 'stunning success' is kidding no-one - that's not giving people confidence in the system".
"They'd like a prime minister who stands up and says 'there are problems and this is what I'm going to do about them'," he added.
Mr Johnson accused the Labour leader of constantly switching from supporting the government to attacking it, with a swipe at Sir Keir's former profession as a lawyer.
"He needs to make up his mind about which brief he's going to take today because at the moment he's got more briefs than Calvin Klein."
A spokesman for the Labour leader said after PMQs: "Keir was raising very serious concerns from bereaved relatives and the prime minister responded with a pre-prepared joke."
What could an inquiry look like?
Independent inquiries can take many forms - from full public inquiries that can take years, or in some cases decades, and cost millions of pounds; to smaller scale, more fleet-footed investigations.
The idea is to hold the powerful to account and try to learn lessons from decisions that have gone wrong, and how to avoid repeating scandals and tragic events in the future.
Recent examples of judge-led inquiries include the Leveson inquiry into media standards, or the ongoing inquiry into the Grenfell Tower catastrophe.
Other inquiries, such as 2009 Iraq inquiry, headed by a retired senior civil servant Sir John Chilcot, do not take evidence under oath.
The government of the day is normally expected to adopt many, if not all, of the recommendations of an official inquiry, although it does not always work out like that in practice.
