British Prime Minister Theresa May will meet opposition Labour Party leader Jeremy Corbyn at 1330 GMT on Wednesday, her spokesman said, adding that further talks could probably be arranged if necessary.
The UK has until 12 April to propose a plan to the European Union - which must be accepted by the bloc - or it will leave without a deal on that date.
The Prime Minister and her government have repeatedly promised Brexit will not lead to a watering down on environmental protections, but there are plenty who fear a shift in policy if she is replaced by a low-regulation hard Brexiter during the next stage of negotiations.
As part of Wednesday's parliamentary business, MPs will also vote on whether to have another round of so-called indicative votes on Brexit Plan B options on Monday.
By approaching Corbyn, a veteran socialist deeply disliked by many Conservatives and mocked by May herself as unfit to govern, she risks enflaming Conservative divisions.
"The Prime Minister's deal won't go through and no deal in law is taken off the table, then the effect of that is either a soft Brexit or no Brexit at all".
"The clock is still ticking, and avoiding a messy and disorderly exit from the European Union is still the top priority for our business communities", Adam Marshall, the head of the British Chambers of Commerce, said after May spoke.
Along party lines, it is clearly split with Conservative Party supporters backing No Deal (72 to 15 per cent) and the left-wing Labour members backing Remain (54 to 21 per cent).
The prime minister's appeal to the opposition Labour Party leader opens the door to the possibility of a much softer form of Brexit, potentially keeping the United Kingdom inside the EU's customs union, in what would be a massive breach of May's own negotiating red lines. May said the government would abide by the decision of the Commons, but only if Labour did so too.
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This is less than Championship clubs Aston Villa, Derby County, Swansea, West Brom, and Stoke City , whose £7.2m tops the league. De Bruyne said: "People ask me what advice I can give, and it's that everyone has to go on their own path". "Yes, of course.
The pound gained 0.3% in early London trading to $1.3187 - its highest since March 28.
Irish Foreign Minister Simon Coveney said Ireland would support a delay but Austrian Chancellor Sebastian Kurz said there was now no reason to agree an extension.
Speaking after the meeting, Mr Corbyn said there had not been "as much change as [he] had expected" in the PM's position.
The Conservatives have been divided over Europe for three decades, leading to the demise of three former prime ministers, David Cameron, John Major and Margaret Thatcher.
Pro-EU lawmakers, meanwhile, sought a legal lock to ensure May could not go back on her promise to seek a delay to Brexit rather than let Britain tumble out of the bloc.
The Withdrawal Agreement brokered by May with the European Union has been rejected three times by the House of Commons.
Professor Matthew Goodwin from the University of Kent at Canterbury told The Telegraph, "These data show significant levels of support for leaving the European Union without a deal, but especially outside of London and also Scotland".
Her decision to work towards a compromise with the left-wing leader has infuriated Eurosceptic Tories as it could pave the way for a softer exit from the bloc. "If I was in Jeremy Corbyn's shoes right now I would be very wary about signing up to anything that may not be able to be delivered, in fact may not be enough in the first place".