Theresa May on Wednesday tried to salvage the British deal to leave the EU in a meeting with opposition leader Jeremy Corbyn where they agreed to work together on a plan, which could leave Britain in a closer relationship with Europe.
“Today’s talks were constructive, with both sides showing flexibility and a commitment to bring the current Brexit uncertainty to a close," a spokesman for Mrs May said.
"We have agreed on a programme of work to ensure we deliver for the British people, protecting jobs and security.”
Hopes to avoid a crash out of the EU on April 12 rose after Mrs May turned towards compromise with the opposition on Tuesday, but doubts remained that a deal could be sealed.
If the talks with Mr Corbyn fail, Mrs May plans to ask Parliament to vote on proposals for the shape of Brexit early next week.
Stephen Barclay, the Brexit secretary, said the government had not ruled out options in advance.
"We're not setting preconditions but nor is it a blank cheque," Mr Barclay said.
Parliament meanwhile considered a bill from backbenchers that would force the government to seek a departure delay from the EU if there were no agreement by April 12.
In a new twist to the drama that has convulsed Westminster for months, MPs brought to a standstill the process of taking control to vote on their own proposals.
The vote was tied at 310-310 and the Speaker cast his vote against more time.
Another amendment brought forward by Labour backbencher Yvette Cooper sought a delay to Brexit and took a no-deal scenario off the table.
It passed by a margin of one vote on the third reading – 313 votes for and 312 against.
The Cooper amendment will become law if the House of Lords passes it in a vote that could happen as early as tomorrow.
Mrs May has faced a move against her from within Conservative ranks. Social media was flooded with images of Conservative membership cards cut up with scissors.
Two members of the government quit, becoming the 35th and 36th members of the administration to leave in the past 12 months.
Chris Heaton-Harris, a junior Brexit minister, said on Wednesday that Mrs May "should have honoured the result of the 2016 referendum" to leave the EU and withdrawn as planned on March 29.
The EU extended that long-scheduled date to April 12 at Mrs May's request, and she says she plans to ask for even more time.
Mr Heaton-Harris published his resignation letter to Mrs May, saying: "Every time we seek an extension to this process we diminish faith in our political system."
Another junior minister, Nigel Adams, resigned earlier on Wednesday over Mrs May's handling of Brexit.
Attorney General Geoffrey Cox, trying to address internal party anger, said Britain could one day review its membership of a possible Customs union after Brexit.
Mr Cox said that while a Customs union might not be desirable, Britain should go ahead if it was the only route to an orderly exit.
"The referendum said leave and leave we must," he said, adding no nation was obliged to remain in such an arrangement for ever.
"If we decided in some considerable years' time that we wanted to review our membership of any such Customs union if we signed it – and I'm not saying we will – that's a matter for negotiation and discussion."
A delegation of smaller parties also met Mrs May but afterwards declared that no agreement was on offer to scrap Brexit through another referendum.
"Given everything we now know, and the detrimental impact Brexit will have on the UK’s economy, job opportunities and people’s livelihoods, the priority must be bringing the issue back to the people in a people’s vote, with the option to remain on the ballot paper," they said in a joint statement.
"We are in agreement that there is no such thing as a good Brexit and that people across the UK face being worse off."
German Chancellor Angela Merkel has reaffirmed her pledge to work "until the last hour" for an orderly Brexit, but says it is mainly up to Britain to provide solutions.
Mrs Merkel said averting a chaotic Brexit was "in the interest of Britain but above all, also in our own interest".