When the eyes of Westminster were on the committee rooms and voting lobbies of parliament this week, Keir Starmer’s political future was being decided elsewhere.

Wes Streeting and Angela Rayner were buttering up Labour MPs in the Strangers’ Bar in parliament as colleagues spoke of their “existential” fear about the crucial elections next week.

Starmer, meanwhile, tried to calm backbenchers’ nerves as he did the rounds in the members-only smoking room and his private office behind the Commons chamber. One former minister said the mood was so dark that several MPs refused to meet the leader, saying: “We don’t want to be seen with him.”

Andy Burnham was 800 miles away in Madrid as Starmer’s future dominated Westminster. But allies of the Greater Manchester mayor were ramping up his leadership campaign and said his return to parliament – and become the next prime minster – could happen “within weeks”.

Burnham has been quietly preparing his manifesto. Those close to the mayor said he would launch an explicit programme for government when he fights his eventual parliamentary byelection campaign, with several possible seats identified in Greater Manchester and Merseyside.

Pledges would include sweeping reforms to the electoral system – backing the introduction of proportional representation across the UK – as well as a decade-long vision to transform local services, higher defence spending and an overhaul of inheritance tax to pay for Britain’s creaking social care system.

Sources close to Burnham told the Guardian he had identified more than one seat that could become available soon after the 7 May elections – and that an “impressive” candidate was lined up to replace him as Labour’s Greater Manchester mayor.

It is understood this candidate is not a sitting MP but is believed to have the pedigree to win a high-stakes mayoral election against Reform UK.

Bev Craig, the leader of Manchester city council, is tipped for the candidacy and is understood not to have ruled herself out. She declined to comment.

“We could get a very good candidate over the line in Greater Manchester. Andy feels confident that can happen,” said one Burnham ally. “There are very strong possibilities of this happening within weeks, but certainly months and over the summer.”

Starmer’s team suggested this week that any attempted Westminster return would be fiercely resisted. Those close to the prime minister have said the prospect of losing the mayoralty is a risk not worth taking – though it is possible that changes to the electoral system in the forthcoming elections bill would give Labour a better chance against Reform in a more proportional voting system.

Members of Labour’s national executive committee, which blocked Burnham from standing in February’s Gorton and Denton byelection, told the Guardian there was no route for the mayor through that committee.

Some allies of Burnham are believed to have been attempting to convince union general secretaries to change their views, with Unison the key target. Others, like GMB, have ruled out supporting Burnham because of his closeness with Ed Miliband, who is at odds with the union over oil and gas licences.

“It would only happen if Keir effectively gave up and said: ‘OK, we’ll let Andy in so I can step down,’” one said. The chances of that happening, according to those close to Starmer, is close to zero.

Yet a growing number of Labour MPs believe this position to be completely unsustainable after a fortnight of damaging headlines over Peter Mandelson and the battering many expect in elections across England, Wales and Scotland next week.

Their fears grew after projections from Robert Hayward, an elections expert, that Labour is expected to lose more than 1,600 seats across England as well as bruising defeats in Wales and Scotland.

Several MPs involved in persuading their colleagues said they believed, with the right numbers, that Burnham would be in place by the autumn.

Some have raised the possibility of Burnham – or another candidate – appointing Starmer as foreign secretary in the next phase to demonstrate consensus.

That would be a highly unlikely outcome, given Starmer’s anger at moves to oust him, and particularly at Burnham’s conduct. “It would allow him to build on his legacy on Iran, on Ukraine, Europe,” one supportive MP said.

The plan, which is said to have the support of some cabinet ministers, would be to issue a statement calling for Starmer to prepare for an orderly departure. MPs expect at least 100 MPs to endorse that after 8 May. “We need to avoid a major internal Labour party row as far as we possibly can, and present it as a fait accompli,” said one MP, optimistically.

“The reason this feels different is because it’s not factional,” one frontbencher said. “It’s not soft left, or SCG [Corbynites] – it’s actually lots of people now coming to make the same point to No 10 that, on 8 May, he needs to set out a timetable to go.”

Another said: “Andy’s standing among Labour MPs is extremely strong. There is a clear view that bringing him into our Westminster team would boost our chances of defeating Reform and preventing Nigel Farage from entering Downing Street at the next election. There is no doubt that he would be able to secure the 80 MPs required in the event of a leadership election.”

They said Starmer had a “great legacy” and had brought the party back together after the fractious Jeremy Corbyn years: “He’s got the chance now to bring the party back together again with a graceful exit.”

Several Labour MPs said the mood had turned “existential” since the Guardian revealed Mandelson had failed security vetting after being appointed as ambassador to the US – a revelation that prompted the sacking of Olly Robbins, the head of the Foreign Office, and two weeks of damaging headlines about Starmer’s judgment.

“Before you broke that story, people were saying it would be difficult for Burnham to come back and that Keir would have until at least Christmas. But that [story] was the straw that broke the camel’s back: now it’s impossible to defend what we’ve seen,” said one MP.

They added: “It feels unanimous now that Burnham is the only game in town with the ability to save their seats, even among people you might have thought would be aligned to other candidates.”

There is significant support for Burnham growing among new intake MPs – but also among the centrist wing of the party. “We’ve spent the last nine months trying to see if something else works – including Keir – and it doesn’t,” said one frontbencher. “This is it – this is the plan. No other plan comes close.”

The soft-left Tribune group of MPs, led by several former ministers including Louise Haigh and Justin Madders, is expected to set out its own call for a change in direction post-May elections.

But MPs who are coordinating the statement demanding an orderly transition say this is a separate endeavour – and reaches all wings of the party. It is also separate to plans to potentially challenge Starmer directly, which would probably shut out Burnham from the contest.

“I don’t want the process to damage us,” one MP said. “I want it to be consensual. He must know things have to change. And, because I support Andy, obviously I think that process should give him a chance to serve then.”

MPs said Burnham had been making considerable effort to meet new MPs – including campaigning in London last week alongside ministers such as Ellie Reeves and Miatta Fahnbulleh.

The more sceptical MPs, some said, were the old guard who had served with Burnham in government. “He only knows about 100 MPs in this parliament and most of them aren’t backing him,” one sceptical minister said.

Nine years after he left Westminster, having served in the cabinets of Tony Blair and Gordon Brown, Burnham could be on the brink of a dramatic return. His team said it was now a matter of “political will” among MPs to bring him back.

“The will that he’s got to be allowed to contest stuff is building and at the same time [Starmer’s] position is weakening,” said one source close to Burnham. “MPs are very despondent, they’re very demoralised. They want an answer to the problems of the existential crisis the party’s facing.”