The boss of Britain’s biggest trade union has endorsed Ed Miliband for chancellor, as the race to take over the Treasury under a potential Andy Burnham government intensifies.

Andrea Egan, the general secretary of Unison, has backed the energy secretary, who is one of two frontrunners to replace Rachel Reeves in No 11, but who is being opposed by two other large unions – GMB and Unite.

The tussle between supporters of Miliband and his most likely rival, Wes Streeting, comes as Burnham prepares to give his first major policy speech since becoming the MP for Makerfield.

The former Greater Manchester mayor will give a speech in Manchester on devolution and the economy on Monday. But he is under increasing pressure to clarify who his chancellor will be, with investors, MPs, unions and business groups arguing it will constitute the most important decision he makes in office.

Egan said: “Andy Burnham has a historic opportunity to rebuild our country in the interests of workers and communities, but that chance will be squandered if his government is made up of politicians determined to continue the same failed approach.

“We need a chancellor who will rewire the economy and properly invest to improve the lives of the majority. Of those reported to be in the running, only Ed Miliband could enact the kinds of policies trade unions and our members urgently need.”

Burnham is in the process of putting together his team of close advisers and ministers, having been elected as an MP a week ago.

Keir Starmer’s announcement on Monday that he intended to resign as prime minister, followed by Streeting’s endorsement of Burnham, has made it overwhelmingly likely the outgoing Manchester mayor will enter No 10 as soon as next month.

Labour’s ruling national executive committee confirmed on Thursday a new leader would be named on 17 July if there was only one candidate. If another MP secures enough support to make the ballot – 81 Labour MPs – the party will hold a leadership election and announce the results on 29 August.

Burnham has chosen his former cabinet colleague and long-term friend James Purnell as his chief of staff, angering some on the left of the party who dislike Purnell’s Blairite roots.

Now however the focus has shifted to who will be Burnham’s chancellor, tasked not only with deciding on possible tax rises in this autumn’s budget but also stimulating growth and overseeing the de-privatisation of some of Britain’s biggest utilities.

The two leading candidates are understood to be Streeting and Miliband, who are from different wings of the party and are likely to pursue different priorities. Streeting, like Purnell, is a Blairite who as health secretary encouraged private sector involvement in the NHS. He is seen as more business-friendly and more likely to reassure international investors, though some on the left fear he will not prioritise taking water and energy companies back under public control.

Miliband is thought of as more ideologically sympathetic to Burnham’s agenda, though has earned anger among some in the unions and the business community thanks to his approach to achieving net zero.

Some investors believe Miliband would be anti-business, pointing to his time as Labour leader when he argued that companies could be classified as either “producers” or “predators”.

Unions with strong representation in the North Sea oil industry have been exasperated by Miliband’s refusal to back down on his promise not to issue new licences in the North Sea.

They also fear he will not approve the Jackdaw and Rosebank megafields in the area, even though doing so would technically not break that promise as they already have licences.

One senior union official told the Financial Times on Thursday: “There are ongoing discussions to try to stop Ed Miliband. There is a GMB-Unite axis on this.”

The endorsement of the general secretary of Unison, which has 1.3 million members, mainly in the public sector, will bolster Miliband’s union credentials. Other smaller unions are expected to come out with similarly supportive messages in the coming days.

Miliband and Streeting are not the only two potential candidates. Other possible choices include Shabana Mahmood, the home secretary, Yvette Cooper, the foreign secretary, Pat McFadden, the work and pensions secretary, John Healey, the former defence secretary, and Jonathan Reynolds, the chief whip.

Allies of the current chancellor, Rachel Reeves, say she would also like to stay in position, arguing she would be able to keep markets calm while giving her full backing to Burnham’s policy platform.

Asked by the BBC on Wednesday about her chances of staying in the cabinet, Reeves said: “I’m not going to pre-empt the decisions that the new prime minister will make. I’m backing Andy and I think he’d be a great prime minister, but those are his decisions, not mine to make.”

She later told the British Chambers of Commerce’s annual conference: “I hope that whoever is chancellor in the future, whenever that future may be, sticks to what I’m doing.

“Because it is beginning to bear fruit, and we are seeing that investment return to the economy, that growth return to the economy, and crucially, that stability, so that businesses can plan and invest in the future.”

Allies of Burnham, however, say he will not keep Reeves in place.