Theresa May is poised to set out the timetable for her departure within days, according to the powerful leader of Tory backbenchers.

The prime minister promised restive Conservative MPs that she would leave Downing Street once the first phase of Brexit had been delivered, but the delay to Britain’s departure from the EU has thrown her future into doubt.

Sir Graham Brady, chairman of the 1922 Committee of Tory MPs, said Ms May would meet with its executive on Thursday after they demanded “clarity” on her plans.

He told BBC Radio 4’s Week in Westminster: “She’s offered to come and meet with the executive, and it would be strange for that not to result in a clear understanding at the end of the meeting.

“We have asked a question. She’s coming, I assume, to answer it.”

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Sir Graham said he believed Ms May was worried that setting a resignation date could derail efforts to get her Brexit deal through parliament.

He said: “I don’t think it’s about an intention for staying indefinitely as prime minister or leader of the Conservative Party.

“I think the reticence is the concern that by promising to go on a certain timetable, it might make it less likely she would secure parliamentary approval for the withdrawal agreement, rather than more likely.”

Ms May has so far refused to say when she will stand down, telling MPs that the Brexit chaos was “not an issue about me” when directly challenged at prime minister’s questions.

The prime minister has also been under renewed pressure to quit after the Tories suffered record losses at the recent local elections.

It comes as Tory leadership hopefuls were openly jockeying for position, with cabinet ministers Rory Stewart and Andrea Leadsom, and former work and pensions secretary Esther McVey, all declaring they would stand.

A string of senior Conservatives are also on manoeuvres, including Sajid Javid, Dominic Raab, Matthew Hancock and Boris Johnson.

Sir Graham, who has chaired the 1922 Committee since 2010, refused to rule out standing for the leadership.

Pressed on the issue, he said: ”It would take an awful lot of people to persuade me.

“I’m not sure many people are straining at the leash at the moment to take on what is an extraordinarily difficult situation.”

He also warned that the cross-party Brexit talks with Labour were destined to “peter out” within days without agreement.

“I find it very hard to see how that route can lead to any sensible resolution,” Sir Graham said.

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“If the customs union is agreed without a second referendum then half the Labour Party won’t vote for whatever comes through regardless, and if a customs union is agreed then most of the Conservative Party isn’t going to support it.

“So, I can’t see that is a very productive route to follow, and I may be wrong, but I suspect it will peter out in the next few days without having come to any significant conclusion.”

Downing Street said the prime minister would stick to her promise to quit as Tory leader once her Brexit deal had been passed by parliament.