Andy Burnham has taken another step towards becoming the next Labour leader and prime minister, after the vast majority of Labour MPs nominated him to replace Sir Keir Starmer.

Burnham’s Labour leadership bid has been backed by 322 Labour MPs as he remains the only declared candidate after nominations began on Thursday.

It makes him just one short of the 323 needed before it is mathematically impossible for a rival to run against him. Some MPs say they were not able to vote on Thursday, but would back Burnham once they are back in Parliament.

If no one else enters the contest, as expected, Burnham will be declared Labour leader next week before taking office as prime minister on 20 July.

It would mark an extraordinary rise to power following the former Greater Manchester mayor’s by-election win in Makerfield just weeks ago.

In a statement, Burnham said he was “deeply grateful” to the Labour MPs who had nominated him to be leader of the party.

He said the support came from across the party and “reflects a shared belief that Britain needs a new approach to politics”.

“That is the circuit breaker I am offering: power out of Westminster, an economy rewired for ordinary people, and good growth in every postcode,” Burnham said.

Burnham’s by-election victory and heavy Labour losses in May’s local elections left Sir Keir facing calls from his own MPs for him to stand aside and allow Burnham to replace him.

Sir Keir quit as Labour leader on the same day Burnham was sworn in as an MP, saying in his resignation speech he had heard the answer to the question of whether “I am best placed to lead us into the next general election”.

Candidates have until Wednesday next week to gather the required backing of 81 Labour MPs in order to take part in the leadership race.

As well as 323 nominations – which is when no one else can reach the 81-MP threshold needed to run against him – Burnham would also need to garner nominations next week from at least three of the 31 socialist societies and trade unions affiliated to the party, although this is expected to be a formality for him.

Burnham would then become Labour leader and be propelled into Downing Street without the need for a vote over the summer among party members and affiliated trade union supporters.

A few dozen MPs had already posted on social media to confirm they are nominating the former mayor.

This included Burnham himself, who joked that it would be “hopefully third time lucky” for him, referring to his two previous failed bids for the leadership in 2010 and 2015.

Burnham’s route to running unopposed was confirmed on Wednesday evening, when former defence minister Al Carns, who had suggested he could throw his hat into the ring, ruled himself out.

But the possibility of a Burnham getting the top job without a contest has already led to some calls within Labour for the ex-mayor to set out further details of the policies he intends to pursue in office.

Burnham left Westminster in 2017, limiting his opportunities to forge strong relationships with Labour MPs elected since then, who now make up the bulk of the party’s contingent in the House of Commons.

As things stand he would be the only participant in an official parliamentary hustings scheduled for Monday next week, at which he would field questions from fellow Labour MPs about his plans for power.

So-called “access talks” with civil servants about his policy proposals are ongoing, run by Cabinet Secretary Antonia Romeo, the UK’s most senior official.

As Labour leadership nominations formally opened on Thursday, Sir Keir said Burnham would make good prime minister.

“I have known him a long time, I’ve worked with him when I first came to Parliament, in his team directly,” Sir Keir said.

Burnham offered some details of his blueprint for office in a speech in Manchester last week, including proposals to establish a new No 10 unit in the city.

He has suggested the unit will be tasked with handing local government more control in areas including housing and transport.

A central part of his policy offering is a pledge to give all parts of the UK “greater public control” of the water and energy sectors, although he is yet to spell out what this would mean in practice.

In a video posted to X earlier, Burnham apologised for Labour’s initial response to Israel’s military action in Gaza, saying the party “didn’t get it right” and needs to do better under his leadership.

And in a Times article on Thursday, external, he also confirmed he wants to keep Sir Keir’s national security adviser Jonathan Powell, a former Blair aide, in post.

He also said he wanted to see a “sustained increase” in defence investment, without committing to a specific target, whilst being “more open with the public” about cost overruns or delays to military procurement.

In one of his final decisions as prime minister, Sir Keir announced a plan to increase military spending by £15bn over the next four years by cutting spending in other parts of government, whilst leaving the details to his successor.