1. Andy Burnham

The Greater Manchester mayor has had nearly a decade to show what he can do with power, and now calls his political philosophy “Manchesterism”. Now he has a path to bring that approach to Westminster.

His signature policy has been to take the city’s buses under public control and link them with trams to form an integrated transport network known as the Bee Network. His allies talk about using that as a model for public services on a national scale as well, especially when it comes to utilities – suggesting more nationalisations would come under a Burnham government.

Burnham has also talked about spending more money on social homes, at the expense of other government-subsidised housing. While this would increase the stock of homes for the poorest renters, it could undermine the government’s overall housebuilding targets, given that social-rent homes require more subsidy per unit.

Last year Burnham spooked investors by saying the UK was “in hock to the bond markets”. He quickly rowed back from suggestions that he wanted a big increase in government borrowing, though he has talked in the past about breaking the fiscal rules specifically to pay for defence.

Possibly the biggest change in a Burnham government, however, would be to the constitution. Burnham has been one of the loudest champions of a more proportional system of voting, and has also promised to abolish the House of Lords and end the whipping system in the Commons that guarantees that MPs of a certain party will vote together.

2. Wes Streeting

The former health secretary’s resignation letter on Thursday fell short of declaring himself a candidate to lead the Labour party, which No 10 sources believe shows he does not have enough support to launch a bid.

However, if he does decide to enter a race at a later stage, he is likely to blend a mixture of traditional Blairism with some of the policy demands of the soft left.

He is likely to push for greater private sector involvement in delivering public services, something he has championed in the NHS, dismissing critics of the plan as “middle-class lefties”.

He has also championed the use of artificial intelligence in the health service, suggesting he would double down on Keir Starmer’s enthusiasm for cutting-edge technology.

Streeting has been one of the most pro-European voices within the cabinet, leaving the door open to the UK rejoining some form of customs union with the EU. He might find that difficult to achieve, however, given the union is likely to demand a high price in return.

On tax, Streeting said years ago he would raise capital gains tax to the level of income tax – something that would constitute a significant increase in tax on wealth. He also said he would replace inheritance tax with a “lifetime gift tax”.

3. Angela Rayner

In the last few months, the former deputy prime minister has made interventions on a range of government policies, giving a sense of what she might do differently if she was prime minister.

Her pet project when she was in government was the package of employment rights she steered through parliament. But the details of many of those rights are still to be decided, and Rayner would be likely to push for the strongest possible interpretation.

She is likely to try to limit the exceptional scenarios in which companies can be allowed to fire and rehire workers, for example, and to push for people to be given as many guaranteed hours as possible under the replacements to zero-hours contracts.

One immediate change is likely to be scrapping Shabana Mahmood’s proposals to make migrants wait for longer before being eligible for settled status. The plan forms the centrepiece of the home secretary’s migration clampdown, but Rayner recently called this “un-British”.

She is also likely to soften the government’s attempts to cut the welfare bill. When the chancellor, Rachel Reeves, previously tried to save £4.5bn by limiting access to disability benefits, Rayner suggested raising the money instead by a range of tax increases, including inheritance tax on shares, stamp duty on commercial properties and taxes on banks.

And while Rayner has said she wants to stick to the government’s borrowing rules, she has also suggested increasing taxes on companies that are benefiting from the Iran war to pay for cost-of-living measures for households. This has led to speculation she could raise the windfall tax on oil and gas producers.

4. Ed Miliband

Miliband has had one of the clearest policy agendas of any cabinet minister since entering government in 2024.

The energy secretary has long put the climate and achieving net zero at the centre of his politics, and has succeeded in persuading the prime minister to face down internal opposition to a ban on new North Sea oil and gas licences.

Fossil fuel companies suspect that a Miliband government would be less likely than a Starmer one to approve the giant new Rosebank and Jackdaw fields, neither of which require a new licence.

Miliband is also likely to increase spending on renewable technologies, having lost a battle in opposition to keep a pledge to spend £28bn a year on green projects.

He has said relatively little about other areas of policy since Labour entered government.

But when he was campaigning to be prime minister as Labour leader in 2015, he ran on a manifesto that included setting the top rate of income tax at 50p and capping how much profit private sector companies could make by providing NHS services.