Nick Eardley,Political correspondentand

Henry Zeffman,Chief political correspondent

The signs are growing that Monday could see the prime minister set out a plan to stand down.

Sir Keir Starmer has always insisted he will not walk away and will fight any leadership challenge.

But the mood in government has shifted in the past 48 hours.

Several government insiders now think that the prime minister could announce a timetable to quit - as soon as Monday.

The signs were clear that things are moving quickly in what Business Secretary Peter Kyle told the BBC this morning.

The prime minister, he said, would do "what is in the best interests of the country".

Sir Keir, he added, was reflecting on the challenges he faces and political realities.

The challenges for the prime minister have been steadily growing for some time.

Labour MPs argue the problem isn't necessarily the party, it's the man at the top. They believe the prime minister is personally unpopular - and that it is Sir Keir who is holding his party back.

The result of the Makerfield by-election looks set to be straw that breaks the camel's back.

Andy Burnham's victory wasn't even close - he beat Reform comfortably. For Labour MPs despairing about how they take the fight to Nigel Farage's party, they now have a leadership contender who can argue he has a track record of doing exactly that.

Dozens of MPs had already said Sir Keir should quit. That list has grown since Thursday, with senior cabinet ministers adding their voices privately.

The fact that it is known that ministers including Foreign Secretary Yvette Cooper, Home Secretary Shabana Mahmood and Transport Secretary Heidi Alexander have told the prime minister to go and yet they remain in their jobs speaks volumes about how Starmer's authority has collapsed.

Burnham is now the overwhelming favourite to be the UK's next prime minister.

If Sir Keir does resign in the coming days, the next question is whether there is any contest at all.

Wes Streeting, the former health secretary, always said he would stand. But his allies are now saying there should be conversations between candidates for No 10 about what the future looks like.

There are some hints a deal could be struck (even if Team Streeting are saying for now that their position hasn't changed).

It is of course possible that someone else throws there hat in the ring - but they won't have long to find 81 MPs to back them to get on a leadership ballot.

The next question is timing - when would the next prime minister take over?

There are disagreements across the parliamentary Labour party about what an "orderly" transition would look like - and specifically how long it would take.

Some influential figures in Burnham's camp want him to take over around the time of the annual Labour conference in late September, believing this would give him more space to prepare for government and ensure he can hit the ground running if he becomes prime minister.

But other leading supporters of the former Greater Manchester mayor believe that timetable is far too slow, arguing that an interregnum of three months would grind government to a halt as speculation about what exactly Burnham's plans for government built into a frenzy.

"His opportunity to define himself would be thrown off by endless speculation," a minister said.

One crucial question which is already the subject of intense speculation is the matter of who Burnham would appoint as chancellor.

In recent days this had been seen by some MPs as a straight fight between Ed Miliband, the energy secretary, and Shabana Mahmood, the home secretary. But Mahmood is now expected to stay in her current role if Burnham becomes prime minister.

The prospect of Miliband as chancellor is causing serious consternation among those on the right of the Labour Party, who would see his appointment as a clear shift to the left.

"If he picks Miliband, about 100 Labour MPs will be furious from the outset," a minister said. Sharon Graham, the general secretary of the trade union Unite, has already publicly urged Burnham not to appoint Miliband.

Burnham and his allies have gone to ground this weekend. They wanted to give Sir Keir time to reflect on the Makerfield result and come to his own conclusion about his future.

There are growing signs that is exactly what is happening. The next few days could be extremely consequential indeed - for the Labour Party and therefore for the country.