Keir Starmer, the British prime minister, is facing increasing pressure to set a date for his departure after elections across much of the country resulted in massive losses for his ruling Labour party.

With the bulk of results now counted after voting on Thursday, Labour had lost more than 1,400 representatives from English councils, the local government structures that deliver many neighbourhood services.

Starmer’s party also crashed to defeat in the election for the devolved parliament of Wales, where it had dominated the country’s politics for a century, and went backwards in representation in the Scottish parliament.

Adding to the panic in Labour, the party lost to a series of challengers, including the rightwing populist Reform UK party, the leftwing Greens, and pro-independence nationalists in Wales and Scotland.

The elections, the biggest since Starmer won power in mid-2024, showed how the UK’s traditional two-party system of Labour and the Conservatives has been smashed, with Reform taking the most votes, and the Greens, Conservatives, Labour and the centrist Liberal Democrats bunched up behind.

While Starmer does not have to face an election to the national parliament in Westminster for three years, increasing numbers of his MPs want him to announce a timetable for his departure, believing he is too politically damaged to turn things around.

Speaking on Saturday morning, Debbie Abrahams, the MP for Oldham East and Saddleworth, an area in the north of England that used to be solidly Labour but has increasingly turned to Reform, said Starmer must “put the country first”.

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

For now, however, Starmer has the backing of his senior ministers, at least in public, including the two routinely named as likely challengers: Wes Streeting, the health minister, and Angela Rayner, who was deputy prime minister until last year.

Complicating matters for any plotters is that the person viewed by many in Labour as the best potential replacement for Starmer, Andy Burnham, is not in parliament. He is the mayor of Greater Manchester and could only return to the House of Commons if another MP stood down and he fought the election to replace them.

Starmer has vowed to fight on. In an opinion article for the Guardian on Saturday, the prime minister said he accepted the results were “very tough”, and that lessons needed to be learned.

But he rejected the argument from some MPs that to recover, Labour must do more to bring back left-leaning voters who have shifted their allegiance to the Greens. He wrote: “While we must respond to the message that voters have sent us, that doesn’t mean tacking right or left. It means bringing together a broad political movement.”

There is a consensus, even among his closest allies, that while Starmer has had some policy successes, and has dealt adeptly with Donald Trump and the wider international situation, his government has made too many missteps and U-turns.

More broadly, many in Labour worry that Starmer is unable to properly challenge either Reform UK, led by Nigel Farage, the politician best known for pushing the UK to vote to leave the European Union in 2016, or the Greens, who have surged in the polls under the leadership of the self-styled “eco-populist” Zack Polanski.

However others in the party argue that changing prime ministers mid-government annoys voters just as much. From 2016 to 2022, the then-ruling Conservatives switched prime ministers four times, and were heavily punished by the electorate at the next election.

Under their new leader, Kemi Badenoch, the Conservatives fared badly in Thursday’s voting, losing more than 500 councillors and giving ground in Scotland and Wales.