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.

Speaking for the government on Sunday, Peter Kyle, the business secretary, refused to comment on Starmer’s specific plans but said the prime minister was aware of the “political realities” and would do what was best for the country.

“I don’t want to come on here and be delusional that there is no process, there are no forces at work which are challenging the prime minister as leader – that is clearly the case,” he told the BBC’s Sunday with Laura Kuenssberg programme.

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

Downing Street reiterated this on Sunday, pointing to Starmer’s comments to reporters on Friday, after Burnham’s byelection win, in which the PM vowed that he would fight any challenge to his leadership.have

Amid hopes on both sides of avoiding too much rancour and confusion, no cabinet ministers have publicly called for Starmer to go. Allies of Yvette Cooper, the foreign secretary, declined to comment on reports that she had privately urged the PM to step aside.

In government, the widespread assumption has spread that Starmer will move on Monday. “I would expect him to do the right thing for the country, with some sort of timetable for departure, most likely around the autumn,” one source said.

While Kyle said he did not know “what the next few days will entail”, he presented Starmer as thinking very carefully about his future and how to avoid damaging the national interest.

Kyle said he had spoken at length to Starmer on Friday. “He was very mindful of the interests of the country, and in that conversation he repeatedly said to me and asked my advice on what I believe the country wanted at this moment in different circumstances.”

Refusing to say what advice he had given, Kyle said of the Labour party: “We are a tight group of people, and we are now facing a period of political uncertainty, and we need to find a way to get through this that puts the country first. This is what we are trying to do.”

Kyle is a close friend of Wes Streeting, who resigned as health secretary last month and has pledged to challenge to become prime minister.

Asked if he would want a full contest to see who might replace Starmer, rather than the mooted coronation for Burnham, Kyle said that while contests were “better wherever possible, that needs to be balanced with the needs of maintaining authority of a party”.

It remains unclear whether Streeting or another candidate or candidates would challenge Burnham should Starmer step aside. Some in Labour believe a contest would help test Burnham and his policy platform, while others worry it could make the government appear gridlocked for weeks.

Streeting 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.

He urged Labour to “learn the lessons of the Tories and make sure that any change that may or may not happen is done in a functional way, and in a way that keeps the government focused on the needs of the people”.

But in a veiled warning to those expecting Burnham to turn around the party’s fortunes, Kyle said Labour also needed to learn from the Conservatives that “whenever they saw a challenge in their party, they always thought that changing the person at the top would fix everything, and that palpably, patently, is not the case”.

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 about 200 Labour MPs, about 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.

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

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 seats.

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 and many Labour MPs are increasingly convinced that without a change of leader, Nigel Farage will win the next election.