Keir Starmer is expected to announce on Monday that he will step down as prime minister, after overwhelming pressure from Labour MPs to make way for Andy Burnham to become Labour leader.

The prime minister and his allies had insisted for weeks that they would fight a leadership challenge from Burnham, or anyone else, before the Makerfield byelection in which Burnham secured a return to Westminster.

But on Sunday morning, the business secretary, Peter Kyle, told Sky News that Starmer was spending the weekend “making time to reflect on the political realities” he faces.

Speaking for the government, Kyle refused to say what he thought Starmer’s plans were, or what he had asked the PM to do.

Asked if Starmer did plan to step down on Monday, Kyle said he had no reason to think this was the case. He said that Starmer would be reflecting on “what putting country first means in a moment like this”.

He did not push back on the idea that a change in No 10 was imminent after Andy Burnham’s big win in Thursday’s byelection.

Saying he had spoken at length to Starmer on Friday, Kyle said: “What I know for a fact is that he has been engaging in conversations with a wide, wide range of people, including myself, and that he is working really hard over this weekend.

“I think he is making time to reflect on the political realities, challenges and opportunities that he finds himself in. You know, I think that is what people would expect him to be doing at this moment in time.”

After the Greater Manchester mayor won Thursday’s contest by a significant margin over Reform, gaining a 9,000-plus majority and more than 50% of the vote, Burnham’s team believed they had the support of around 200 Labour MPs, around half the parliamentary party.

That number has since increased, with Burnham becoming increasingly confident of a coronation in which he would take over as Labour leader and thus PM without a contest, with Starmer setting out a relatively quick timetable for departure.

On Friday, ministers previously loyal to Starmer told him that he should reach a decision on a timetable for his departure by the end of the weekend or face being forced out of office, with an intervention at Tuesday’s cabinet meeting likely to result.

Any MP who wishes to challenge to be leader needs the backing of at least 20% of the parliamentary party, or 81 MPs.

Wes Streeting, the former health secretary, who resigned last week in frustration at Starmer’s leadership, has pledged to seek the top job and says he has sufficient backers, but allies of Starmer and Burnham are sceptical. His candidacy will become less likely if wavering Labour backbenchers conclude that they would prefer to back a likely winner and swing behind Burnham.

Starmer’s departure will set the UK on course for a seventh prime minister in 10 years, just two years after he led Labour to a sweeping general election victory, winning a majority of 174.

But his premiership has been battered by controversies and U-turns, including over winter fuel payments to older people and the decision to appoint Peter Mandelson as UK ambassador to Washington.

Labour has slumped in the polls, and Starmer himself is enormously unpopular with much of the public. Reform UK has led for more than 300 consecutive national polls, with many Labour MPs increasingly convinced that without a change of leader, Nigel Farage will become the next prime minister.