Attention is therefore increasingly focused on what Burnham in No 10 would look like.
On his policy and priorities, there are still a lot of questions in search of answers. We are starting to get some answers on his top team, however.
Rachel Reeves will not be his chancellor. That is hardly a surprise for an incoming prime minister vowing to offer change.
But it is still a big deal: Reeves has not only been chancellor for two years but spent years in opposition fashioning Labour’s economic approach.
She is likely to be offered a more junior cabinet position – though it is worth noting how rare it is for a chancellor to move downwards in the cabinet.
With the exception of Nadhim Zahawi, who spent a few brief weeks as Boris Johnson’s chancellor, you have to go back to 1983 for an example of a chancellor moving into a more junior cabinet job.
So who replaces her?
The frontrunner is widely considered to be Ed Miliband, the energy secretary. He urged Sir Keir not to block Burnham’s first attempted return to Parliament in January and has been seen as supportive of Burnham’s ambitions ever since.
Miliband’s advocates argue that he is exactly the kind of chancellor Burnham would need to make good on his ambitions to transform the British economy.
They also argue that – whatever MPs think of his agenda, particularly on the green transition – he has shown in the past two years an uncommon ability to drive the government machine. He also has years of Treasury experience advising Gordon Brown.
But there are many Labour MPs, especially on the right of the party, who are opposed to the idea.
Some of that is animosity lingering right back to his years as leader. But their bigger concern about Miliband is policy: for some he would represent a shift too far to the left.
“I think the chancellor thing is a huge risk for Andy,” says one MP.
“If Andy goes through with Ed it will divide the party from the start,” says another.
What about Wes Streeting? He has been talking up his economic credentials in recent weeks, arguing for a vision of “progressive capitalism” – and his allies are lobbying for him to get the keys to No 11.
They argue he would be a “sensible choice” who could reassure financial markets. They also claim his communication skills would mean he would be able to sell big economic ideas at a human level.
But there are big risks too. “Wes wants to be prime minister one day. Would Andy ever be able to trust that Wes would have his back when things are tough?” asks a minister.
Other names doing the rounds include Yvette Cooper, the foreign secretary who like Burnham is a former chief secretary to the Treasury, and John Healey, the ex-defence secretary – though appointing him would commit Burnham to a large increase in defence spending.
