Ed Miliband has privately suggested to Sir Keir Starmer that he should consider setting out a timeline for his departure amid concerns he will be forced out of No 10 after the election results, The Times has been told. 

Two sources familiar with the discussion said that the energy secretary and former Labour leader made the suggestion during a private meeting with the prime minister about a fortnight ago.

While Miliband remains supportive of Starmer he is concerned that Labour will descend into a bitter and damaging leadership contest in the wake of the elections, which are expected to be disastrous for Starmer.

Angela Rayner, the former deputy prime minister, and Wes Streeting, the health secretary, are both said to have the support of the 81 Labour MPs needed to trigger a contest. Rayner is considering making a move despite the fact she has not been cleared by HM Revenue & Customs over her tax affairs.

Miliband is viewed by allies as a “kingmaker” to a potential run for the leadership by Andy Burnham. Burnham, the mayor of Greater Manchester, is understood to have told supporters in recent days that a backbench MP is willing to stand down as soon as this weekend to facilitate his return to Westminster.

Angela Rayner, former UK Deputy Prime Minister, smiles during the National Growth Debate in London.Angela Rayner THOMAS KRYCH/ANDALOU/GETTY IMAGES

Miliband has ruled himself out as a candidate to succeed Starmer but is increasingly concerned that the prime minister may not survive to fight the next election.

Labour is facing historic election losses as the results are announced over the next two days. It could finish third in Wales, where it has been the dominant party for more than a century, and third in Scotland. It faces losing as many as 1,800 councillors in the local elections in England as it haemorrhages support to Reform UK, the Greens and independent candidates.

The aftermath is expected to prompt increasing calls from senior Labour figures for a change in leadership and result in some MPs calling for an immediate challenge to Starmer.

Miliband was said by colleagues to be “very down” and privately in despair over the probable scale of Labour’s losses to Reform UK and the Greens. 

Miliband will join cabinet loyalists in backing Starmer this weekend, but he has significant concerns about the risk of Labour descending into a civil war and the damage it would do to the party and the government unless the prime minister sets a timeline for his departure.

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He is understood to have raised his concerns during a private discussion with Starmer during which the two men talked about potential options for the aftermath of the elections.

Miliband is supporting a return to Westminster for Burnham as the left-of-centre candidate best positioned to restore Labour’s fortunes. Starmer remains intent on blocking a Burnham comeback and has made clear that he will not set out a timeline for his departure. 

Andy Burnham speaking in Brixton, London, with people holding "Pride in Lambeth" signs in the background.Andy Burnham needs to return to Westminster before he can challenge for the leadershipBetty Laura Zapata FOR THE TIMES

A source close to Miliband said that he was not the “despairing type” and had been on the campaign trail fighting for votes and supporting the prime minister.

A spokesman for Miliband would not comment on “private conversations” but said: “We do not accept this account.” He did not dispute that the discussion had taken place and declined to say how the accounts differed.

“Ed has always supported the prime minister and continues to do so as he delivers on his mandate for change,” the spokesman said.

The Times understands that Burnham has told several Labour MPs on Merseyside and in Greater Manchester that a backbencher is willing to resign their seat to facilitate his comeback. Those who have spoken to the mayor said an announcement could be made as soon as Saturday. 

Marie Rimmer, 79, the MP for St Helens South & Whiston — close to Burnham’s former constituency of Leigh & Atherton — is believed by colleagues to be the likeliest candidate. Burnham has dismissed those suggestions as “fiction”. 

Secretary of State for Energy and Climate Change Ed Miliband, Prime Minister Keir Starmer, and Jacob Collier, MP for Burton and Uttoxeter, meeting with Universal Credit claimant Nicola Saint at her home.Miliband and Starmer discuss the government’s warm home plans with householders in Staffordshire last yearCHRISTOPHER FURLONG/Getty IMAGES

The mayor has nonetheless emerged as the preferred candidate of powerbrokers on Labour’s soft left, who believe an orderly transition to his leadership over a period of months is the only way to avert a bloody civil war.

Ministers and MPs who support Burnham fear that a leadership challenge from Streeting will trigger a tit-for-tat challenge from Rayner and a chaotic exit from No 10 for Starmer. Instead they support backbench efforts to force the prime minister to name a date to depart on his own terms, allowing Burnham time to return to the Commons and succeed without a contest.

Rayner will “take the temperature” of colleagues before deciding whether to mount a formal challenge. The Times understands that she does not see the fact that HMRC has yet to conclude an investigation into whether she paid enough stamp duty on a flat in Hove as a barrier to putting herself forward.

Allies said she was ready to go and was confident she would get the backing of the 81 MPs needed should a putsch be launched in the wake of the local election results.