Keir Starmer is expected to announce a timetable for his departure on Monday morning, clearing the way for Andy Burnham to become prime minister without a formal contest by the autumn.

Cabinet ministers say Starmer will set out his intentions outside No 10 Downing Street, starting a process of the UK installing its seventh prime minister in a decade.

No 10 officials were still insisting Starmer stood by his pledge on Friday to fight an anticipated leadership challenge from Burnham, who returned to Westminster via an overwhelming win in the Makerfield byelection.

But with more than half a dozen cabinet ministers having privately told him his time is up – and the additional pressure of a hostile cabinet meeting on Tuesday – the prime minister spent the weekend at the Chequers country retreat finalising a likely exit plan.

While other options remained open, Starmer and his inner circle began work on drafts of a resignation speech on Saturday, with the most likely timetable involving him staying in office until the autumn, allowing a new leader to rally Labour troops at the party’s annual conference at the end of September.

It is understood that he will do so without having had a discussion with Burnham about his plan since the Makerfield result.

“Logically the best thing for both Andy and Keir would be for that to happen in September,” one cabinet minister said. “Andy has no team ready to go into Downing Street and needs the time to prepare. It would also allow Keir to establish a flight path to his departure.”

One obvious uncertainty is whether Burnham would be the only candidate, allowing an effective coronation, or if other challengers will emerge and gain the necessary support.

Wes Streeting, who resigned as health secretary last month amid efforts to push Starmer to quit, said last week he would stand in any contest and had the necessary backing of 81 MPs to do so, with allies saying over the weekend that this was still the plan.

Some MPs say they would welcome a contest to allow Burnham’s platform to be tested. There is, however, an increasing presumption that Streeting will not compete, either because he does not have the MPs needed or because he would almost certainly lose a vote of Labour MPs and would be wary of derailing preparations for the next government.

If Streeting did challenge Burnham, it is possible that others may seek to join in, notably one or more women in the cabinet to prevent an all-male contest.

Despite Starmer saying he would speak to Burnham after the weekend, it is understood he may decide not to, and that he has not talked to Streeting. Some of Starmer’s inner circle believe that setting out his arrangements for departure unilaterally would allow him to claim he was doing so on his own terms.

A government source said an autumn date nonetheless seemed most likely: “I very much expect Keir to do what is best for the country, and Andy currently does not seem ready.”

A later date is unlikely, given the need for time to prepare for a politically crucial budget later in the autumn.

Early preparations for a possible handover have already begun, with Darren Jones, the chief secretary to the prime minister, meeting Louise Haigh, a key member of Burnham’s team, and further talks are expected.

While Starmer has thus far avoided any ministerial resignations since the Makerfield result, or even any new public calls for him to go, seven cabinet ministers are known to have told him since the May local elections that he should consider his future for the sake of the party and the country.

One cabinet minister said: “There was a view that resignations would be required if Keir’s public view – that he would fight any challenge – remained his private view.” But over the course of Sunday, they said, “a shift appears to have taken place in his mind” which made this less likely to happen.

Even late last week, some friends of Starmer remained insistent he should fight on, and that it was hugely presumptuous for Burnham and his team to expect a prime minister who won a landslide majority less than two years ago to step aside for a regional mayor out of parliament since 2017.

But as the very obvious lack of support for Starmer became more clear, even allies began to accept there was a new reality.

Sent out to speak on behalf of the government on Sunday, Peter Kyle, the business secretary who is loyal to Starmer, was forced to admit, even tacitly, that the PM’s days seemed numbers.

“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.

Kyle said he had spoken at length to Starmer on Friday and offered him advice, declining to say what this was. Starmer was, Kyle explained, “very mindful of the interests of the country”.

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.”

Asked if he would want a full contest to see who could replace Starmer, rather than a 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”.

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”.