Theresa May is to meet the chairman of an influential committee of backbench Tory MPs, Sir Graham Brady, amid calls for her to set a firm resignation date.
It follows a request from the 1922 Committee for “clarity” on the issue.
No 10 insists the meeting is routine, but pressure is mounting on the PM, with local Tory associations confirming they will hold a vote of confidence in her leadership on 15 June.
Meanwhile, cross-party talks to break the Brexit deadlock are due to resume.
In March, Mrs May pledged to stand down if and when Parliament ratified her Brexit withdrawal agreement with the EU – but she has not made it clear how long she intends to stay if no deal is reached.
The UK had been due to leave the EU on 29 March, but the deadline was pushed back to 31 October after Parliament was unable to agree a way forward.
On Monday, Sir Geoffrey Clifton-Brown, treasurer of the 1922 Committee – an elected body of MPs which represents backbenchers and also oversees leadership contests – told the BBC that Mrs May should announce a “road map” for her resignation after the European elections set for 23 May.
No confidence vote of Tory MPs: Theresa May won a leadership ballot by 200 to 117 votes on 12 December 2018. Under current party rules, there can’t be another vote for a further year so the PM is technically safe until 12 December this year. Many MPs want to change the rules to allow an earlier contest but this would need to be agreed by the 1922 Committee.
No confidence vote in Parliament: The PM would have to resign if she lost a confidence vote in Parliament. Labour tried this manoeuvre in December but Tory MPs and their DUP allies backed the PM. Might some Tories now withhold their support if they think it will usher in a new leader rather than a general election?
Grassroots Tory revolt: Local Conservative associations seem to be turning against the PM, with one – Clwyd South – already passing a motion of no confidence in her. The National Conservative Convention’s vote on 15 June is non-binding, though, so the PM could ignore it.
Cabinet revolt: Margaret Thatcher quit in 1990 after a number of ministers told her it was time to go. Could history repeat itself? There has been no sign of that so far and colleagues who want to succeed her – and there are many – may not want to be seen to be the ones wielding the knife or to risk sacrificing their own careers.
Quits of her own accord: The BBC’s Norman Smith says there is no way the PM will “walk away” right now, but this could change in the aftermath of a “catastrophic” result in European elections.
Leading Eurosceptic Sir Bill Cash also told the Press Association “the time has come” for her to resign.
“She needs to be given a date. The sooner the better. But it needs to be done in an orderly manner,” he said.
But Chancellor Philip Hammond defended the PM’s attempt to do a Brexit deal with Labour, suggesting the government had no other option.
“The most important thing is that we put in place arrangements which allow us to have as low-friction trade as possible between the UK and the EU,” he said during a visit to Paris.
“Of course we should talk to the Labour Party about that.
“We tried to get a deal through Parliament. We weren’t able to get a parliamentary majority so we now have to find a compromise that can get a parliamentary majority.”
Pressure is building on Mrs May following last week’s local election drubbing, in which the Conservatives lost 1,334 councillors in England.
In an unprecedented move, the National Conservative Convention – the most senior body within the voluntary party – is to hold a vote of confidence in her leadership next month.
The vote was triggered after 65 local Conservative associations said they had lost trust in the prime minister.
The prime minister has blamed the Brexit impasse for her party’s terrible performance last week and urged Labour, which itself lost 82 seats, to compromise to agree a deal.
Will the cross-party talks get anywhere this week?
No 10 is trying to get Labour over the line by presenting the withdrawal agreement as a stepping stone – i.e. hold your nose for now and you can carve out your own deal if you win the next election.
Key to that is the promise of a “temporary customs union” – but Labour sources warn if that’s all it is, that’s what’s already in the withdrawal agreement anyway (plus a few months) and doesn’t add up to anything substantially new.
A senior government source says it IS possible, though, to see a way to a deal, but it is unlikely to be resolved this week – and their aim is not to create some kind of May-Corbyn Rose Garden moment (imagine!) but to set out a path to get the Withdrawal Bill to Commons with a fair wind.
Reports emerged at the weekend that the prime minister was ready to offer a temporary customs arrangement with the EU that would last until the next general election.
Labour has previously said it wants a permanent customs union – an arrangement not to carry out checks or put tariffs (extra payments) on goods that move around an area.
A number of senior Tory Brexiteers have said they would not vote for a customs union.
And Brexit Party leader Nigel Farage said by pursuing a customs union and following single market rules, the two main parties were “forming a coalition against the people”.
“It is very clearly not what the people voted for,” he said at an event in London, where he announced the new party was starting to recruit candidates for a future general election.
Labour MP Mary Creagh told BBC Radio 4’s Today the PM’s authority had been fatally damaged and suggested her party “needs to be wary of the embrace of a drowning woman”.
She urged Jeremy Corbyn to recognise the results of last week’s elections and “listen” to Labour members, who she said were overwhelmingly in favour of another referendum.