Britain has repeatedly stated that, following Brexit and as a newly independent coastal state, it wants to be in control of its waters and fish.
European fishing vessels fish six times as much in UK waters as British vessels do in EU waters, which means the UK has leverage in the talks.
Brexit negotiations have been deadlocked for months over the issue of fishing rights with talks coming down to the wire ahead of the transition deadline of December 31.
Time is tight to secure a free trade deal between the two sides, with the transition period set to end in just over a month.
Talks stretched late into the night as both sides fought their corners with the clock ticking down to the deadline for a trade deal.
It was reported that several boxes of pizza were delivered to the talks venue on Wednesday night as officials from London and Brussels tried to hammer out an agreement ahead of the end of the transition period on December 31.
READ MORE: Brexit LIVE: Boris 'sadly mistaken' if he thinks he can 'betray fishermen'
"It's about making sure that the UK is able to run its own laws, its own fisheries and so on."
It comes amid warnings talks with the EU have reached a "make or break" point.
Mr Barnier is said to have warned that significant differences remain over fisheries, state aid rules and the governance arrangements for any agreement.
He said negotiations on a trade deal with Britain were reaching "a make-or-break moment", and they urged him not to be rushed into an unsatisfactory agreement.
While both sides have acknowledged that time is running out, there has been no sign that either is prepared to make a decisive move that could resolve the issue one way or the other.
On Tuesday, French President Emmanuel Macron sounded a warning that he would not accept an agreement that "would not respect our interests in the long term" amid concerns in Paris that Mr Barnier is preparing to give ground over fishing rights.
The news highlighted France's determination to defend access to British waters for French fishermen during talks over Britain's future relationship with the EU.
There are fears in France of a major surrender from Mr Barnier in what would be the first major concession from the bloc in talks on their new relationship after the UK finally unshackles itself from the bloc.
https://news.google.com/__i/rss/rd/articles/CBMifWh0dHBzOi8vd3d3LmV4cHJlc3MuY28udWsvbmV3cy91ay8xMzY3NzYwL2JyZXhpdC1sYXRlc3QtbmV3cy1icmV4aXQtZmlzaGluZy11ay1ldS1icmV4aXQtbm8tZGVhbC1ib3Jpcy1qb2huc29uLW1pY2hlbC1iYXJuaWVy0gGBAWh0dHBzOi8vd3d3LmV4cHJlc3MuY28udWsvbmV3cy91ay8xMzY3NzYwL2JyZXhpdC1sYXRlc3QtbmV3cy1icmV4aXQtZmlzaGluZy11ay1ldS1icmV4aXQtbm8tZGVhbC1ib3Jpcy1qb2huc29uLW1pY2hlbC1iYXJuaWVyL2FtcA?oc=5
2020-12-03 08:54:00Z
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