May now gambles on last-minute softer Brexit deal

But fury inside her own party and from her Northern Irish allies could also prompt snap elections and a no-deal exit on 12 April.

May announced her gambit after seven-hour long, but inconclusive, talks with her cabinet ministers in London on Tuesday and after MPs rejected a series of Brexit proposals on Monday.

"Today I am taking action to break the logjam: I am offering to sit down with the leader of the opposition and to try to agree a plan that we would both stick to, to ensure that we leave the European Union and that we do so with a deal," she said.

"The ideal outcome of this process would be to agree an approach ... that both the leader of the opposition and I could put to the house for approval, and which I could then take to next week's European Council," May added, referring to an emergency EU summit in Brussels on 10 April.

"I've always been clear that we could make a success of no-deal in the long term, but leaving with a deal is the best solution," the prime minister said.

For his part, Corbyn agreed to hold talks on Wednesday.

"I recognise my responsibility," the leader of the left-wing Labour Party said.

The talks opened the door to a softer Brexit than that envisaged by May's Conservative party.

Corbyn has in the past said the UK ought to stay in a permanent customs union with the EU and to have the same relations with the single market as those it has now. He also wants workers' rights in the UK to be continuously aligned with those in the EU.

The new talks were greeted with caution by EU officials, who previously said they would need strong reasons to extend the 12 April deadline further.

"Even if, after today, we don't know what the end result will be, let us be patient," EU Council president Donald Tusk said.

The French and German foreign ministers, speaking to press from a UN meeting in New York, were more critical of the British confusion.

"We are five minutes past midnight and this should be known in London," Germany's Heiko Maas said.

"Honestly, it's sometimes difficult to follow," France's Jean-Yves Le Drian said on the twists and turns of the Brexit debate in London.

"Three years after their decision, it would be great if they had a clear position. Otherwise, a hard Brexit will have to take place in the coming days," he added.

But back in London, May's appeal to Corbyn was seen as a betrayal by the eurosceptic wing in her party, auguring a potential collapse of the government.

"You do find that leaders who decide to go with the opposition rather than their own party find their own party doesn't plainly follow," Jacob Rees-Mogg, a Tory MP who leads an anti-EU faction in May's party, said.

Boris Johnson, a Tory MP and former foreign minister, said a deal with Corbyn would make Brexit "soft to the point of disintegration".

The Northern Irish Democratic Unionist Party, which props up May's minority government in Westminster, added: "It remains to be seen if sub-contracting out the future of Brexit to Jeremy Corbyn, someone whom the Conservatives have demonised for four years, will end happily."

Meanwhile, if the Corbyn talks failed, May said she would put "a number of options for the future [EU] relationship" to "a series of votes" in parliament "to determine which course to pursue."

"Crucially, the government stands ready to abide by the decision of the house," she said on Tuesday.

But that failed to reassure business groups, given that parliament had failed to agree on any course of action over the past three years.

"The clock is still ticking, and avoiding a messy and disorderly exit from the EU is still the top priority for our business communities," Adam Marshall, the head of the British Chambers of Commerce, said after May spoke.