If Andy Burnham moves from Manchester to No 10, he will be the first prime minister to have been health secretary in the history of the NHS. What might that mean for the troubled service? His commitment to social care is well known. But when the Treasury tells him there is no money, he is going to have to think hard about how to make his mark.

The UK now spends the fifth most of any OECD economy when it comes to government health spending as a proportion of GDP. That’s why health service insiders no longer say the issue is money but productivity. They have been puzzling over why, since 2020, the total number of staff across NHS England has grown by 20% but activity has only gone up by 10%. That’s part of the reason why waiting lists have remained stubbornly high and a significant part of the progress made in reducing them has come from “list cleaning” – removing people from lists who no longer need treatment – rather than actual increases in activity.

Getting to the bottom of this matters because there isn’t likely to be a lot of extra cash soon. One reason for inefficiency is poor IT, which is why, as chancellor, in my 2024 budget I gave the NHS £3.4bn for a new productivity plan that included the joining up of medical records and embrace of AI. But that won’t be enough because it won’t tackle the root cause of NHS inefficiency.

And the reason is something that the former mayor of Greater Manchester will be very familiar with. As mayor, if Burnham needed money for a big infrastructure project, he had to bang on the door of No 11 and get in a Whitehall queue.

But what he experienced in Manchester is also a daily reality across NHS England, which is the most centralised and bureaucratic healthcare system in the world: 1.5 million people are micro-managed from London with 18 monthly operational targets for hospitals and 44 “QOF” (qualities and outcomes framework) targets annually for GPs upon which their income depends. Every new health secretary is told by No 10 to “grip” the service. Every time, the response is a new target.

The result is learned helplessness by local managers. They are micro-managed to deliver “improvement trajectories”, leaving them little time for the innovations that boost productivity.

For that reason, I hope that as prime minister Burnham would consider a much bigger structural reform. First, he should scrap all national targets. It’s something I wanted to do as health secretary as soon as we got back to hitting targets that were being missed – something that sadly never happened. Second, Burnham should look at devolving responsibility for the NHS in different areas to the locally elected mayors who are now being rolled out across England. That would follow the regional model used in Sweden and Denmark, both of which have universal systems but with much better outcomes than the NHS.

But we don’t have to look abroad to see how this would work. We don’t have national targets for the number of A-level passes in maths or physics but instead give state school heads a high degree of autonomy. Accountability comes through Ofsted inspections and the publishing of exam results. And the result? England now has the highest reading standards in the western world.

A hospital in Barrow-in-Furness faces different challenges from one in central London. A rural integrated care system serving dispersed communities faces different pressures from one serving a large metropolitan population. There should be national standards, including maximum waiting times, but maximum autonomy in delivering them.

Manchester was supposed to have this with “Devo Manc” in 2016. But national targets remained. Hospital bosses were accountable not to the mayor but to NHS England. The impact was far less than originally hoped.

Now is the chance to finish the job. And if, at the same time, social care were handed to mayors in the areas where it is not already within their remit, it would help improve that too. Governments have been trying to break down the barriers between the two services for years. Now it might finally happen. It wouldn’t, of course, solve the funding problems in social care but it would help in other ways, not least by making it much easier for hospitals to end “bedblocking” by discharging patients promptly.

There are many issues on which I profoundly disagree with Andy Burnham’s soft-left worldview. But on this we might just agree. Both of us have sat on top of the pyramid as health secretaries and seen how difficult it is to make an enormous system responsive to patients. Both of us have wanted to be the health secretary who finally “fixed” the NHS from the top – and found we could not. But as prime minister, this is something Burnham really could do. It would turn the NHS from the world’s most bureaucratic health service into its most innovative one. And what other options are there in a world where there is no extra money?

• Jeremy Hunt served as secretary of state for health, later secretary of state for health and social care, from 2012 to 2018