MPs from Labour’s left are expected to urge Ed Miliband to consider a leadership bid in the coming days, as Keir Starmer faced the prospect of a definite challenge from his MPs next week.

Following grim results for Labour in elections on Thursday, the former minister Catherine West said that if no cabinet ministers went public by Monday, she would launch a bid to end the impasse.

A series of Labour backbenchers called on Saturday for Starmer to set a timetable for his departure from Downing Street. The prime minister has reiterated his determination to stay on, saying on Saturday that a change of leadership would “plunge the country into chaos”.

A number of Labour MPs from across the party support Andy Burnham replacing Starmer. However, the Greater Manchester mayor requires a time-consuming and uncertain byelection to re-enter parliament.

There has been speculation that Wes Streeting might be considering a move next week, although the health secretary’s allies have vehemently denied this and point to his public support for the PM on Friday.

With any route for Burnham back to the Commons still unclear, dozens of backbenchers from the party’s left are now preparing to turn to Miliband. The group is expected to urge the energy secretary to step in and prevent a Streeting coronation, believing that Angela Rayner, Starmer’s former deputy, does not have the necessary support.

MPs were weighing up their options a day after Labour’s disastrous election results, with some backbenchers adding their voices to calls for the prime minister to go. But matters began moving at speed, with West, a north London MP who Starmer sacked as a Foreign Office minister last year, telling the BBC that in the event of no other challengers, she would ask colleagues on Monday to back her as a way of starting a contest.

She said she had the support of 10 MPs so far, well below the required 81 – 20% of the parliamentary party – to endorse any challenger. But her action could prompt others to act.

“My preferred option is for the cabinet to do a reshuffle within itself, where there’s plenty of talent, and for Keir to be given a different role, which he might enjoy, perhaps an international role,” West said.

She added: “I don’t have a candidate. That’s part of the problem. But I think there are several people who would like to do it, who have been planning for months, but I’m very surprised that none of them has popped up today to say, ‘I will do it.’”

Labour lost more than 1,400 councillors across England on Thursday, shedding support to Reform UK and the Greens in traditional heartlands. In Wales, the party lost power for the first time, plummeting to just nine Senedd seats behind Plaid Cymru and Reform, while also losing ground in the Scottish parliament.

Starmer, who is due to make a speech on Monday about closer European links, began a fightback on Saturday with two new appointments he characterised as “future-looking” – involving the Labour grandees Gordon Brown and Harriet Harman.

Brown, the former prime minister and long-serving chancellor under Tony Blair, has been made Starmer’s envoy on global finance, with a brief to advise on financial partnerships to help defence-related investments, particularly with Europe.

Harman, who was Labour’s deputy leader under Brown, will be the prime minister’s adviser on women and girls, focusing on tackling violence and improving economic opportunities.

Speaking on a visit in south London earlier in the day, Starmer said that while he accepted he had to “rebuild” after the losses, he would not step down: “I’m not going to walk away from this. That would plunge the country into chaos.”

Other Labour MPs have called on Starmer to set a date to hand over the leadership, including Clive Betts, the long-serving Sheffield South East MP, and Debbie Abrahams, for Oldham East and Saddleworth.

Abrahams said: “We have to recognise the dangers that we’re in now, that on this trajectory it doesn’t look good..” Asked how quickly he should consider departing, she added: “I think it is a matter of months.”

In a post on X, Tony Vaughan, the Labour MP for Folkestone who was first elected in 2024, said there “must be an orderly transition of leadership well before the local elections next year”.

Another 2024-intake MP, Terry Jermy, released a statement saying Starmer “needs to consider whether he is the right person to take the party and the government forward”.

Meanwhile, one of Labour’s most powerful figures outside Westminster, the West Yorkshire mayor, Tracy Brabin, told the government it faced “oblivion” at the next general election without a renewed “boldness” from ministers.

Brabin described the local election losses as “catastrophic” after Labour lost overall control of several councils in her region to a Reform UK surge.

Brabin stopped short of calling for Starmer to stand aside but said: “This is a catastrophic set of results for the Labour party. Here in West Yorkshire, and across the country, we’ve lost dedicated councillors who have served their communities tirelessly without self-interest … Two years on from a landslide general election victory, the Labour party is facing oblivion if these results are repeated. We cannot waste the opportunity of Labour being in government.”

Additional reporting by Josh Halliday