'We are now at a particularly critical stage in these negotiations,' said a spokesman for British Prime Minister Theresa May on Monday
The EU's chief Brexit negotiator Michel Barnier meets Britain's negotiating team on Tuesday as both sides seek a breakthrough with just weeks to go before this month's ominous divorce deadline.
The sit down comes after Barnier said on Saturday that the European Union was ready to give London further guarantees to help push a troubled divorce deal through the British parliament.
Barnier also suggested European leaders would be amenable to a short "technical" delay in Britain's departure from the EU, scheduled for March 29, to give parliament time to formally ratify a final divorce deal.
His small overture to Britain has raised hopes that both sides can find a solution, including to the so-called "backstop" plan for the Irish border, a major sticking point for pro-Brexit MPs.
Barnier, a former French foreign minister, will meet in Brussels with Britain's attorney general Geoffrey Cox and Brexit minister Stephen Barclay for talks that start at 1600 GMT.
"We're now at a particularly critical stage in these negotiations," said a spokesman for British Prime Minister Theresa May on Monday.
'Running the show'
Cox's presence is seen as central to the meeting, as he will ultimately offer a legal opinion on the Brexit deal and the Irish backstop that could determine whether key MPs in the British parliament will approve the accord.
Earlier disfavourable advice by Cox was viewed as a contributing factor in the defeat of May's deal by MPs in January.
"Cox is running the show," a senior EU source told AFP.
"We are trying to find a junction between our positions and we are not there yet," the source added.
But despite that defeat, EU leaders insist that the withdrawal agreement will not be reopened, and talks in Brussels are focused on drafting a separate document to placate doubters in London.
Also raising hopes are the softening positions of several hardline Brexit supporters in May's Conservative party who have dropped their demand that changes to the backstop be made to the withdrawal treaty itself.
But most of them continue to press for a time limit or exit clause to the backstop. They have also set up a team of lawyers to scrutinise anything that Cox brings back from Brussels.
"Many Tories who dislike May's deal are reluctantly coming round to the idea of voting for it," said Eurasia Group analyst Mujtaba Rahman, a former UK official.
"Regardless of what he gets" from Barnier, "Cox will reverse his previous legal advice that the UK could be trapped 'indefinitely' in the backstop," Rahman predicted.
In 2017, Britain invoked Article 50 of EU law, triggering a two-year countdown to Brexit that ends at 2300 GMT on March 29.
Both sides are furiously trying to steer away from a dreaded "no-deal" divorce with the EU that could wreak havoc on global markets and create border chaos.
British MPs last week agreed to give May more time to get her changes from Brussels, but if she cannot get her deal passed by March 12, she has agreed to let parliament vote for a possible Brexit delay.