Theresa May will set out the timetable for her departure following one final attempt to get her Brexit deal passed by MPs.
The prime minister held talks with senior Conservatives in Westminster on Thursday, where she was pressed for more clarity on her timetable for exiting Downing Street.
Sir Graham Brady, chairman of the 1922 Committee of backbench Tory MPs, said he will meet Mrs May to agree the details of her exit from Downing Street early next month.
This will come after a showdown vote on the Withdrawal Agreement Bill, which enshrines the PM’s Brexit plan into UK law, in the week beginning 3 June.
Sir Graham said: “The prime minister is determined to secure our departure from the European Union and is devoting her efforts to securing the second reading of the Withdrawal Agreement Bill in the week commencing June 3 2019 and the passage of that Bill and the consequent departure of the United Kingdom from the European Union by the summer.
“We have agreed that she and I will meet following the second reading of the Bill to agree a timetable for the election of a new leader of the Conservative and Unionist Party.”
Sir Graham characterised the talks with Mrs May as “very frank” – and confirmed his next meeting with her would take place regardless of whether the Withdrawal Agreement Bill passes.
One Brexiteer Conservative MP said the announcement, which means the PM has again resisted calls to name the date of her departure, showed the 1922 Committee was “absolutely weak”.
“They’re going to split this party down the middle,” they added.
Earlier this year, Mrs May promised to go once her Brexit deal has been passed by MPs.
But with this looking like an increasingly remote prospect, growing numbers within her party have been pushing for a more specific timetable for when she will quit.
The PM’s Brexit deal has been defeated three times by MPs, with the trio of reverses prompting her to request a delay to Brexit.
Britain was originally due to leave at the end of March, but this has now been pushed back until October.
This delay has provoked fury among the Tory grassroots, with the febrile atmosphere not helped by the party’s poor performance in the local elections.
The party also appears to be on course for a bruising night in next week’s European elections at the hands of Nigel Farage’s Brexit Party.
The 1922 Committee’s announcement will ratchet up the jostling and jockeying to replace Mrs May in Downing Street.
Former foreign secretary Boris Johnson confirmed an open secret in Westminster earlier when he said he would put himself forward to replace her as Tory leader.