As he swept towards victory in the Makerfield byelection, Andy Burnham told voters he wanted to see “the essentials of life being run primarily for the public interest, not for the private interests”.

Citing the Bee Network of buses and trams across Manchester city region, brought together on his watch, Burnham repeatedly highlighted the need for more “public control” over the necessities of life. Water, energy, transport and housing are at the top of his list.

Now PM-in-waiting, he is expected to say more about his economic priorities in a speech on Monday.

Burnham’s Manchester address will garner intense interest, from his more leftwing backers to the owners of vast chunks of the British economy. They will be trying to gauge whether he is really serious about expanding the role of the state – all the way through to outright nationalisation – and willing to stare down the vested interests standing in the way.

His choice of chancellor is being viewed as a critical test of his radicalism on this agenda. Advocates of an economic reset, including nationalisation, see Ed Miliband as the only plausible candidate who would be prepared to countenance the steps needed – including facing down intense industry lobbying.

Former health secretary Wes Streeting, by contrast, did not mention public ownership or control in his recent speech on “progressive capitalism”, with the bookies’ favourite for No 11 focusing instead on alignment with the EU, planning deregulation and exploiting the North Sea.

Neal Lawson, the director of the progressive thinktank Compass and a vocal supporter, sees the distinction between public control – which could just mean tougher regulation, for example – and full-blooded public ownership, as key.

“Does Andy Burnham think he can go for ‘control,’ when all of the evidence suggests these things are uncontrollable, and can only be managed in the public interest by being owned in some innovative way by the public sector?” he says.

Perhaps the most radical vision of what public ownership could mean was set out in a dense policy paper published recently by Mat Lawrence, director of the Common Wealth thinktank, under the auspices of Burnham campaign vehicle Mainstream.

Lawrence says of Burnham: “He’s grasped that part of people’s desire for change is this hybrid and bureaucratic model we have for essential sectors, with a weak state trying to regulate privatised utilities, which doesn’t really work for anyone, in terms of affordability, investment, sovereignty, or quality of life.”

Common Wealth was set up explicitly to make the case for greater public ownership – though Lawrence and his co-author Alex Williams eschew the word “nationalisation”.

Their central argument in the paper, The Productive State, is that many of the basics of life – including transport, energy and water, but also social care and housing – have become too expensive, because shareholders are forever taking a slice.

That leads to higher inflation, they say – and therefore higher interest rates; and leaves voters frustrated that basic public goals, such as keeping England’s waterways free of faeces, seem forever out of politicians’ reach.

Cat Hobbs, the founder of the We Own It campaign, which has long argued for public ownership of key resources, stresses this latter, democratic aspect of the argument.

“The arguments are fairly straightforward,” she says. “We’re talking about natural monopolies. We don’t have choice as consumers, and so what we’ve argued is that we need accountability as citizens.”

Common Wealth insists its favoured approach has little in common with the postwar model of great, clunking nationalised industries, funded directly by the Treasury and with ministers in command.

Instead, they hark back to an earlier example – the Central Electricity Board, established by Stanley Baldwin’s Conservative government in 1926. The state-owned arm’s-length body built the first national grid, and rationalised electricity generation, helping to drive down bills.

Research by Arthur Downing, of the LSE, has shown that the regional public electricity generators of the time, known as “municipals”, were able to cut prices, because they did not need to pay out profits to shareholders, and could borrow more cheaply than a private operator could.

Somewhat similarly, Common Wealth describes the model it has in mind as “the public corporation, operating with a clear mandate, borrowing against its own revenues, insulated from both Treasury short-termism and shareholder extraction.”

As Burnham prepares to move into No 10, the future of Thames Water is seen as an early test case, with ministers set to decide whether the heavily indebted company should collapse into the state’s special administration regime (SAR) or its bondholders be allowed to take it over.

Thames’s shareholders have already been wiped out, and its creditors have offered to take a hefty discount. SAR can be used to tip a firm that provides a crucial public service, and is at risk of collapse, into a form of temporary insolvency. An independent administrator would then take over negotiations with lenders.

The expected outcome after a company has gone into the SAR is for it to be sold back into the private sector once its finances have been restructured. But advocates of nationalisation argue that ministers could instead mandate that Thames ends up a public corporation.

Even Lawrence, who believes public sector ownership could and should be much more widespread, is cautious about how rapidly this process could take place – conscious of the risk of alarming private sector investors.

“This is not against markets, or dynamism, or entrepreneurialism; it’s about fixing some of those sectors that are not working to provide the affordable foundations for dynamic businesses to thrive,” he says, arguing that state capacity – the ability for the public sector to run things – has to be built up slowly.

Indeed, in the three years left of a Labour administration, Lawrence reckons Thames might be as far as the government could get, in terms of nationalising existing utilities – though Hobbs, and campaigners at the thinktank Compass, would like to see a much more aggressive use of the SAR.

Even that would be less drastic than the approach favoured in Labour’s 2019 manifesto, which was to take “rail, mail, water and energy” into public hands, by exchanging government bonds for shares. Jeremy Corbyn’s Labour insisted the plan would be “fiscally neutral” because the state would acquire assets, though the Institute for Fiscal Studies put the upfront cost at “many tens of billions” and pointed out the taxpayer would also be taking on hefty debts.

That same approach – bonds for shares – is the one laid out in the Productive State paper.

Fresh borrowing to fund such a process could be accommodated under the current fiscal rules, if the state acquires a financial asset in return. But that would not apply to the firms’ physical assets, creating potential accounting headaches, unless the rules were rewritten again.

It could also result in lengthy legal battles over what constituted fair value to investors.

The government’s relatively straitened fiscal position, with the debt-to-GDP ratio tripling in the past 20 years to 96% and a debt interest bill of £137bn due this year, also raises questions about the potential cost of additional borrowing.

For these and other reasons, Lawrence suggests Burnham should focus for the moment on quick(ish) wins that lean towards public “control” as well “ownership”.

All metro mayors could be encouraged to use franchising powers to create Bee Network-style integrated transport networks, while the government’s Great British Railways could take more action to coordinate routes and fares across the train operators Labour is returning to state ownership.

Meanwhile, a string of development corporations, with borrowing powers, could be set up to kickstart housebuilding, rather than hoping that planning deregulation alone will fuel a construction renaissance.

Rachel Reeves has already announced the creation of a development corporation for Greater Cambridge.

Lawrence suggests Labour could then go into the next general election advocating a more thoroughgoing nationalisation agenda, that could include taking the energy transmission companies into state ownership.

Another often-cited vehicle for change is Great British Energy: advocates of nationalisation argue this state-owned vehicle has been set up too timidly, and could enter the energy generation business, if it was scaled up and given a more expansive remit.

Burnham’s campaign rhetoric about an expanded role for the state could encompass a wide range of possibilities. With his top team set to be announced shortly, the MP for Makerfield’s every word will be watched intently, to determine whether he is ready, as the title of Miliband’s relentlessly upbeat book put it a few years ago, to “go big”.