Andy Burnham now has a potential route back to parliament and a chance to become Labour’s next leader after an MP said he would trigger a byelection by standing down from his seat.

The move ended days of speculation about whether Burnham could secure a possible path back into Westminster and underlined the increasingly precarious nature of Keir Starmer’s premiership.

In a day of high drama, Wes Streeting quit as health secretary after seemingly failing to get the numbers to launch a challenge against the prime minister. Meanwhile, Angela Rayner was cleared by HMRC over her tax affairs, paving the way for her own return to frontline politics.

But it was the announcement by a Greater Manchester MP that he would be standing down, triggering a byelection, that finally brought some clarity to the chaos that has engulfed the Labour party since last week’s crushing election results.

Burnham, the Greater Manchester mayor, confirmed he would ask Labour’s ruling national executive committee (NEC) to allow him to stand in the contest. Allies of Starmer confirmed that he would not seek to block him, after MPs across the party shared their concerns.

Burnham said “much bigger change is needed at a national level”, singling out the cost of living crisis as a priority for his campaign in a statement that set out why he wanted to return to Westminster.

“This is why I now seek people’s support to return to parliament: to bring the change we have brought to Greater Manchester to the whole of the UK and make politics work properly for people,” he added.

Burnham has been seeking to return to parliament for months, but was prevented by Starmer from running in the Gorton and Denton byelection at the start of this year, to the anger of his backers in the party.

The next full meeting of Labour’s NEC is due to be held next Tuesday, but two sources said the 10-person officers’ group, which will confirm Burnham’s selection, could meet as soon as Friday.

Starmer’s authority has been critically undermined in recent days after an angry response from Labour MPs to last week’s local and devolved elections, including the resignation of Streeting and other ministers, and about 100 MPs calling for him to go.

A number of cabinet ministers have admitted privately that they believe Starmer will not lead them into the next election, with three telling the Guardian they believed he would be forced to oversee a smooth transition of power to Burnham instead.

The decision by Josh Simons, the MP for Makerfield, which Labour holds with a majority of slightly more than 5,000, paves the way for a crucial byelection in the Greater Manchester seat, where Reform UK came second last time.

Nigel Farage said his party would “throw absolutely everything” at the contest in what will be an attempt to derail one of Labour’s biggest figures, stalling his path to power. Reform regards Burnham as a far tougher opponent than Starmer, with more cross-party appeal.

The contest will not be straightforward. While Burnham won the constituency in the 2024 mayoral race with 62% of the vote, at last week’s local elections Reform won 50.4% across the eight wards up for election, with Labour trailing on just 22.7%.

In a letter to constituents announcing his decision to stand down, Simons said: “I do not believe this government is delivering the urgent, radical, brave reform we need. We need a new direction. I believe that Andy Burnham can provide it.

“I could not stand here and tell you that our politics is broken and things need to change, then stand in the way of supporting that change.”

A byelection contest takes about five to six weeks, meaning the earliest Burnham could return to parliament would be early July. With backing right across the party, he could trigger a leadership contest, which he would be expected to win, potentially unchallenged.

Angela Rayner and Ed Miliband are understood to support the idea of Burnham running for the leadership, while Streeting said any contest “needs to be broad, and it needs the best possible field of candidates”, a signal he would back the mayor running.

One senior Burnham backer told the Guardian: “If you’ve got people from Angela to Wes saying it, then the whole party is now in the same place on this. Andy needs to be given a shot. He is the person that connects best with the public.”

Burnham’s announcement came hours after Streeting, his most likely rival for the leadership, quit as health secretary and called for the prime minister to resign.

In a letter to Starmer, he said: “Where we need vision, we have a vacuum. Where we need direction, we have drift … Leaders take responsibility, but too often that has meant other people falling on their swords.”

Crucially, however, he did not declare his candidacy for the leadership, and even appeared to make a coded message of support for Burnham.

“Labour MPs and Labour unions want the debate about what comes next to be a battle of ideas, not of personalities or petty factionalism,” he wrote. “It needs to be broad, and it needs the best possible field of candidates.”

On Thursday evening, James Murray was appointed as health secretary, moving from his role as chief secretary to the Treasury, as Starmer declined the opportunity to bring a leftwinger into the role after Streeting’s departure.

Starmer’s allies said they believed Streeting did not have the support of 81 MPs needed to trigger a leadership contest and that his endorsements totalled 44 at most. Streeting’s friends have denied this, however, insisting he did have the support but wanted Starmer to resign rather than triggering a potentially messy contest.

Burnham allies told the Guardian that no deal had been done in advance with the Greater Manchester mayor, but some in Westminster have speculated Streeting might be brought back if Burnham becomes prime minister.

Angela Rayner told the Guardian that Starmer would have to “reflect on” whether he should step aside, adding that Burnham should not have been prevented from re-entering parliament last time.

“If somebody wants to come and help, and be part of the future that we can deliver, then absolutely we shouldn’t be blocking people … We cannot afford to be factional about this. We cannot afford to have egos,” she said.

The former deputy prime minister has been cleared by HMRC of deliberate wrongdoing or carelessness over her tax affairs, and has settled £40,000 in unpaid stamp duty, but avoided any penalty as a result of the investigation. It means she could now return to a cabinet role.

Lucy Powell, Labour’s deputy leader, is expected to tell the FBU conference on Friday that the election results had been “deeply painful and difficult” but that the aftermath has been “unedifying”.

“We don’t do hostile takeovers in Labour for a reason. Keir is the leader, and I warned against bloody internal battles reflecting badly,” she added.

“If we think we don’t have further to fall, that’s a mistake; we can. We must come back together as one team to take the fight to Farage and show that mainstream progressive politics can bring about the change people are crying out for.

“That also means doing politics differently. Ending briefing wars, ending factionalism, and representing all our traditions with our strongest team on the pitch … Andy Burnham, Wes Streeting and Angela Rayner should all be key players in our team.”