Theresa and Jeremy Corbyn fired broadsides in a Brexit blame game after crunch talks aimed at striking a compromise collapsed.
The Prime Minister claimed Labour splits over a second EU referendum torpedoed hopes of reaching an agreement which could pass the Commons.
But Mr Corbyn hit out at the Prime Minister’s “weakness” after she caved into backbench demands to plan a timetable for her resignation.
The failure to crack the deadlock after six weeks of tense talks paves the way for Mrs May to suffer a fourth and final humiliating defeat on her Brexit pact – forcing her out of No10.
Campaigning in Bristol for next Thursday’s European Parliament elections, the PM claimed: “We have not been able to overcome the fact that there is not a common position in Labour about whether they want to deliver Brexit or hold a second referendum which could reverse it.”
It had become increasingly clear in Westminster over the past fortnight that talks were doomed.
No10 finally accepted on Thursday night negotiations had reached “the end of the road”, a source revealed.
The admission came less than 12 hours after Mrs May tearfully bowed to demands and agreed to set a timetable for her departure in the first week of June.
But her capitulation fuelled Labour fears any pact it struck would be torn up by her successor.
Mr Corbyn hammered the final nail into the coffin at 10.39am Friday as he published a letter to the PM confirming he was collapsing negotiations.
He told her: “It has become clear that, while there are some areas where compromise has been possible, we have been unable to bridge important policy gaps between us.
“Even more crucially, the increasing weakness and instability of your Government means there cannot be confidence in securing whatever might be agreed between us.”
He cited Mrs May’s looming exit from Downing Street, which triggers a leadership race Boris Johnson is favourite to win.
“As you have been setting out your decision to stand down and Cabinet ministers are competing to succeed you, the position of the Government has become ever more unstable and its authority eroded,” wrote Mr Corbyn.
“Not infrequently, proposals by your negotiating team have been publicly contradicted by statements from other members of the Cabinet.”
The Downing Street source admitted the talks’ breakdown was “disappointing” and pointed the finger of blame at Shadow Brexit Secretary Sir Keir Starmer.
Sir Keir, who is seen as a vocal supporter of a second referendum, is tipped as a potential successor to Mr Corbyn and led talks for Labour.
The source said it was “obvious” there was a “significant difference of opinion” in the Parliamentary Labour Party on a second referendum, adding that divisions were apparent among Labour’s negotiating team.
“It is clear and has been for the duration that these talks have gone on that there are fundamental splits in Labour, particularly on the question of a second referendum, which breaks down to the choice between whether to honour the referendum or hold a second referendum in an attempt to reverse it,” said the source.
“It is clear, for example, that the Shadow Brexit Secretary has fairly strident views on this issue and he represented and led the Labour team during the ministerial plenary sessions, for the most part.”
The source said that if the Withdrawal Agreement Bill fails to clear the Commons before the summer recess, “the choice will become significantly more unpalatable, because the arguments about no-deal and whether or not to revoke Article 50 entirely will become more vociferous”.
Second referendum campaigners seized on the breakdown and issued fresh demands for another vote.
Labour MP Stephen Doughty said: “The only way out of this Brexit crisis is to put this back to the people in a confirmatory public vote so that the people get the final say on the future.”
Naomi Smith, of the anti-Brexit Best for Britain campaign, said: “It’s clear from the breakdown in talks that neither party leader can sell their own version of Brexit to their respective parties.
“Labour must now stand firm on its commitment to back a public vote and make it crystal clear that the party won’t engage in any more Westminster back room talks.”
The Withdrawal Agreement Bill is set to be voted on the first week in June.
Labour has played down suggestions it could abstain and effectively usher through the legislation, with senior frontbenchers insisting they will try to vote it down.
But some backbenchers from Leave-supporting heartlands are likely to back the PM’s deal and honour the 2016 result.
Mrs May’s spokesman pointed to “real progress on some issues such as workers’ rights and environmental protections” made in negotiations before talks were axed.
That could help some Labour MPs support the Bill – though there are unlikely to be enough to cancel out Tories who will oppose the legislation.
He added: “The PM continues to believe it is the duty of elected politicians to find a way to deliver on the result of the referendum.
“She continues to work hard on securing the passage of the Withdrawal Agreement Bill so that the UK can leave the EU with a deal as soon as possible.”
When Brussels issued an Article 50 extension to October 31 – delaying Brexit – EU Council President Donald Tusk urged: “Please do not waste this time.:
No10 insisted six weeks of talks with Labour had bene “absolutely in the national interest”.
The PM and Mr Corbyn met face-to-face three times for talks, with further discussions over the phone.