0547 GMT January 26, 2020
Labour Party leader Jeremy Corbyn said the gaps between them could not be bridged – and he had no confidence that her successor would stick to any bargain they might have reached, AFP reported.
The discussions have "gone as far as they can," Corbyn said in a letter to May.
"The increasing weakness and instability of your government means there cannot be confidence in securing whatever might be agreed between us," he said.
Corbyn said Labour would therefore continue to oppose the government's EU divorce deal as it stands.
MPs three times rejected the deal May struck with Brussels, forcing her to delay the date of Brexit twice and to reach out to Labour.
MPs are due to vote for a fourth time in early June on the terms of Britain's withdrawal from the EU.
An ashen-faced May said they would be faced with a "stark choice": voting to deliver Brexit, or "to shy away again".
On Corbyn's announcement, she said: "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."
She was speaking at a rare campaign event ahead of the European Parliament elections, to be held in Britain on Thursday, in which polls suggest her Conservative Party could even come fifth.
Britain was never meant to take part in the elections but will do so because of the postponements to Brexit.
The collapse in talks came the day after May agreed to set out a timetable for her departure following the withdrawal agreement vote in Parliament, set to take place in the week beginning June 3.
The arrangement was agreed in a meeting with the 1922 Committee of backbench Conservative MPs.
It is thought that May will trigger a leadership contest once the Withdrawal Agreement Bill either falls, as seems likely, or reaches completion.
The timetable is likely to mean a new Conservative leader, and therefore prime minister, should be in place before the party's annual conference in September.
Former foreign secretary Boris Johnson is the bookmakers' favorite to replace May. He revealed Thursday that he would run.