Theresa May has been warned by an influential Tory MP to set a date for her resignation – or risk being toppled by her backbenchers.

Former Tory Party chairman Grant Shapps says that unless the Prime Minister announces a timetable for the end of her ‘uninspiring’ leadership, she could soon face a vote of no confidence.

His powerful intervention comes as the party is convulsed by plots, feuds and increasingly outspoken criticism of Mrs May by Tory MPs dismayed by her botched reshuffle.

The febrile atmosphere has been intensified by the need for the Government to set out its vision of an ‘end state’ for Brexit to EU negotiators within the next month – triggering open Cabinet battles between ‘soft’ Brexiteers such as Chancellor Philip Hammond and the hard Brexit camp led by Foreign Secretary Boris Johnson.

Former Tory Party chairman Grant Shapps says that unless the Prime Minister announces a timetable for the end of her ‘uninspiring’ leadership, she could soon face a vote of no confidence

Last night, an ambitious Tory MP tipped as a future leader added his voice to the chorus of disapproval – warning unless improvements were made Jeremy Corbyn would win the next Election.

Plymouth MP Johnny Mercer told The Mail on Sunday: ‘We need to be doing better, or we will pay the price.’

Mr Shapps reveals that several Tory MPs are this weekend sending letters to Sir Graham Brady, the Chairman of the party’s 1922 Committee, calling for a leadership contest.

If Sir Graham receives a total of 48 letters, he is obliged under party rules to spark that contest with a confidence vote.

Sir Graham has not revealed how many letters he has received, but senior sources believe that it was already ‘nudging 40’ before the latest batch went in this weekend.

At least three new MPs are thought to be writing to Sir Graham this weekend.

So who's first in line to step in and take over? Our very rough guide... Boris Johnson (left) and Jeremy Hunt (right) Amber Rudd (left) and Michael Gove (right) Jacob Rees-Mogg (left) and David Davis (right) Sajid Javid (left) and Dominic Raab (right) Priti Patel (left) and Gavin Williamson (right) Andrea Leadsom (left) and Tom Tugendhat (right) Penny Mordaunt (left), Justine Greening (centre) and Nicky Morgan (right) Advertisement

Mr Shapps has not yet sent a letter himself, because he says he feared that a leadership contest would destabilise the Government. But friends say that after Mrs May’s reshuffle earlier this month – notable for Health Secretary Jeremy Hunt’s refusal to move jobs – Mr Shapps’ stance is shifting.Writing in this newspaper, he says that Mrs May’s loss of authority was making it ‘excruciatingly difficult’ for her to ‘demand obedience from her own Cabinet’.

The Welwyn Hatfield MP said that it was ‘becoming increasingly clear day by day that we cannot continue to muddle along like this’ and Mrs May should ‘name a date’ and ‘do so before it is too late’. Mr Shapps dismisses the argument used by many May loyalists that she should not go before Brexit in March 2019 – pointing out that Neville Chamberlain was replaced by Winston Churchill when we were at war with Germany in 1940.Downing Street ‘outed’ Mr Shapps last October for collecting a list of the names of Tory MPs who were privately saying that Mrs May should stand down – but had not necessarily written to Sir Graham. Mr Shapps says he was trying to ‘control the process’ so that any bid to start a leadership contest could be timed to the maximum advantage of the party.

It is understood that Mr Shapps made clear to Downing Street that he would not send his own no-confidence letter if No 10 worked with him to ‘gauge the mood’ in the party – but the offer was rebuffed.

Captain Mercer, a former Army captain who entered the Commons in 2015, warned that unless the Government’s performance improved the party could face electoral wipeout.

The Afghanistan veteran said: ‘We need to be doing better, or we will pay the price with the electorate. We have to face down some of the very clear challenges on the NHS, housing and defence.’

Asked about Mrs May’s performance, he stopped short of calling for Mrs May to step down, saying: ‘I’m not going to comment on the Prime Minister.’ The botched reshuffle – and lack of clarity over Brexit – have stirred resentments on the backbenches among even normally loyal MPs.

Captain Mercer, a former Army captain who entered the Commons in 2015, warned that unless the Government’s performance improved the party could face electoral wipeout

Mark Pritchard, MP for The Wrekin in Shropshire – who once called for rebellious colleagues to be sacked – said this weekend: ‘There is a growing frustration that No 10 is not plugged in to the views and opinions of many backbench MPs or even interested.

‘The PM is also being criticised for taking her very small group of allies for granted. A big mistake.’ Mrs May’s most senior Cabinet Ministers are becoming increasingly entrenched in their positions on Brexit.

Mr Johnson was rebuked by fellow ‘soft’ Brexit Cabinet Ministers last week – led by Mr Hammond – when he pre-briefed a Cabinet call for a Brexit dividend for the NHS. He is also planning to set out his personal vision for a ‘clean’ EU withdrawal next month.

Mr Hammond then caused fury among the Brexiteers when he claimed last week that Brexit would involve ‘very modest’ changes to the status quo.

Leading Brexiteer Jacob Rees-Mogg has accused the Government of a ‘timid and cowering’ approach to the Brexit talks. He warned: ‘The leader is important but the party is more important. Brexit is more important than anyone other than the Queen.’