Labour MPs who were previously loyal to Keir Starmer are now deserting him as calls grow for the 'lame duck' Prime Minister to cede power to Andy Burnham within weeks.

Sir Keir has repeatedly vowed to fight any challenge to his leadership and insisted he will not 'walk away'.

But Mr Burnham's stunning victory in the Makerfield by-election has unleashed a fresh wave of demands for the embattled PM to quit Downing Street, with the number of Labour MPs calling for Sir Keir to resign topping 100.

Labour grandees, including some Cabinet ministers, have told Sir Keir that his time is up following Mr Burnham's thumping win.

Transport Secretary Heidi Alexander is among those understood to have told Sir Keir on Friday that he needed to set out a timetable to quit this summer.

A senior Labour source told the Daily Mail that the PM will face a showdown at Tuesday's Cabinet meeting unless he had agreed to step down by then.

Labour peer Lord Falconer on Saturday admitted the party's leadership chaos was 'completely unmaintainable' for the country and told Sir Keir - who he said had been left with 'absolutely no authority' - to agree to go before MPs leave Westminster for their summer break next month.

Meanwhile, some Labour MPs who signed a letter rejecting calls for a leadership election last month, in the wake of the party's local elections meltdown, have now reversed their position.

Sir Keir is expected to spend the weekend at Chequers weighing up his future – and wargaming how to deal with a potential wave of ministerial resignations next week. 

Peter Swallow, the Labour MP for Bracknell, was one of those to sign a statement in support of Sir Keir following the local elections in May.

But he told BBC Newsnight that 'it is now the right time for the PM to resign and hand over to someone else' and that he'll be 'backing Andy'.

Asked what had changed since he said in the aftermath of the May elections that it was no time for a leadership contest, Mr Swallow said the 'final straw' for him was 'when John Healey resigned as Defence Secretary.'

He added 'frankly our inability to agree a Defence Investment Plan in a timely fashion was for me the last straw' and that we 'now need to look to the future and move forward as a party in the best interests of the country.'

Mr Swallow said that he was 'proud of all the things we've achieved in the last two years' but that sometimes his constituents 'haven't always felt the change that we've been delivering.'

He said it was 'really important that we can have someone who can tell the story of what we're doing' and 'that's why I'll be backing Andy.'

Asked when he would like to see a new PM by, he replied: 'In the country's interests a swift transition is what we need.'

Lord Falconer, a former Cabinet minister, also put pressure on Sir Keir to agree to hand over power to Mr Burnham before Parliament's summer recess begins on 16 July.

He told BBC Radio 4's Today programme on Saturday: 'We have to move as quickly as possible to resolve the position.

'The position is completely unmaintainable for the country. We have a prime minister who has got absolutely no authority.

'The reason he has got no authority is because everyone assumes Andy Burnham is about to challenge for the leadership. And everyone assumes he's going to win.

'So if you've got a Prime Minister who has only got - at most - weeks to go, he is not able to control his Cabinet, he is not able to command the Commons, he is not able to deal with our allies and - indeed - our enemies in a way that is required.'

Lord Falconer urged Mr Burnham to trigger a leadership election by getting the required 81 Labour MPs to nominate him as a challenger to Sir Keir.

And, although Sir Keir can automatically enter a leadership contest under Labour Party rules, Lord Falconer advised him not to do so and to stand aside.

'My advice, sadly, would be don't stand,' he added. 'Because if you stand it is likely there would then be a very difficult leadership battle in which the two leadership candidates will try to undermine each other.

'That would be bad for the country, it's also bad for the country that there would be this further delay.

'The timing of this, I think, should be as follows; Andy should indicate he's running... by the beginning of July we would know as a country who are the runners and riders.

'If Keir doesn't stand, then there'll only be one runner and rider. There should be an agreed transition process in which Andy and Keir cooperate as to when the handover should take place.

'Speaking entirely for myself, I think the best time for the handover would be before the parliamentary recess, which is on the 16th July.'

Lord Falconer suggested Mr Burnham had enthused previously-despondent Labour MPs with his victory over Reform UK in Makerfield.

'You cannot underestimate the extent to which the mood, the buzz that Andy Burnham has created is very, very strong,' he said.

Allies of Mr Burnham are said to favour a longer wait for him to become PM to allow them to prepare for government.

Former transport secretary Louise Haigh, one of Mr Burnham's key supporters, said after his by-election victory: 'We really hope that this can be a managed and orderly transition and Keir Starmer will reflect on the results, and Andy and Keir can meet in the coming days, and over the next week, and agree a path forward.'

Mr Burnham's camp is said to want Sir Keir to set out his plans in the coming days but would accept a timetable that kept him in No10 until September.

But former deputy leader Harriet Harman has urged the party to move faster, telling Sky News that ministers could not be left 'in a state of paralysis all through the summer'.

Makerfield had been billed as a tight contest, but Mr Burnham won comfortably with 55 per cent of the vote. 

In the wake of the by-election, Sir Keir appeared to be digging in. He warned Labour staffers during a call on Friday lunchtime to avoid 'plunging our party and our country into chaos by turning on each other and tearing apart our party and our movement'.

The PM is said to have amassed a campaign war chest to fight any leadership challenge with the backing of a group of private donors.

Fundraising has ramped up in the last two days with total pledges running into six figures, sources said.

Allies of Wes Streeting, the former health secretary. said he was still set on forcing a leadership contest to ensure any new PM had a mandate for their ideas for the country. 

Sir Keir and his backers in the Parliamentary Labour Party have stressed the need to focus on the by-election for the Greater Manchester mayoralty triggered by Mr Burnham's election.

That by-election is scheduled to take place on July 30, with Labour set to announce its candidate on June 26.