Update: The news has been confirmed in a statement from the 1922 Committee.
This is @theresa_may clinging on to a semblance of control over the manner and timing of her departure. But it confirms that her resignation date will be announced within a very few short weeks pic.twitter.com/6G6NcQEr29— Robert Peston (@Peston) May 16, 2019
Key line from Sir Graham Brady's statement: “We have agreed that she and I will meet following the 2nd Reading of the Bill to agree a timetable for the election of a new leader of the Conservative and Unionist Party.”— Jack Maidment (@jrmaidment) May 16, 2019
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After a day of meetings with Tory backbenchers, Graham Brady, the leader of the influential Tory 1922 Commission, reportedly told a reporter from ITV that May has agreed to resign next month even if her Withdrawal Agreement fails to pass during its fourth go-round in the Commons
BREAKING: Sir Graham Brady tells us that PM is expected to resign whether or not the WAB passes in June. A leadership election this summer is now a dead cert.— Paul Brand (@PaulBrandITV) May 16, 2019
The report has been confirmed by the BBC and the Telegraph, and is being taken seriously by the rest of the British media. Of course, it's possible that May could deny it but her talks with backbenchers have been widely followed all day and there was some expectation that they would strike some kind of a deal over her resignation.
Source confirms implication of agreement btw Brady + May - if 2nd reading passes, PM stays on to fight next stages thro Commons, in hope that we leave EU before recess, if it fails, which at this stage is a LOT more likely, she's gone, contest over summer, new PM at Tory conf— Laura Kuenssberg (@bbclaurak) May 16, 2019
Sir Graham Brady says he will agree a timetable for a Tory leadership election with the PM after MPs vote on the Withdrawal Agreement Bill in the first week of June.— Jack Maidment (@jrmaidment) May 16, 2019
Means PM is going regardless of if she wins the WAB vote.
It was reported earlier this week that May would bring her widely hated withdrawal back for an unprecedented fourth vote in the Commons, and that she is in talks with Labour to try and convince the opposition to abstain from the vote, which would increase the odds of the agreement passing.
The reaction in cable was muted, but the currency has been drifting lower all week in what has become its longest losing streak since 2000.