After Brexit, David Cameron’s second worst legacy is his assault on the NHS. His explosive 2012 Health and Social Care Act was designed to privatise it into small pieces, while an eight-year funding drought yields new worst ever figures every month. The wonder is that the service still treats so many so well. The number of GPs fell again last month, while graphs for nurses, emergency doctors, ambulance staff and just about everything show a relentless downward trend. Waiting times for cancer treatments rise, as do delays to treating older people’s hip fractures after falls.

The NHS is now the top cause of public anxiety, according to Ipsos Mori. Is there any good news? There is: the Institute for Fiscal Studies finds a continuing steep rise in NHS productivity, treating ever more people, far outstripping dismal overall UK productivity rates. Hold on to that fact, as the usual NHS detractors scent blood in the water, claiming the system itself is broken and needs private insurance or top-up payments.

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Here’s a Sunday Telegraph editorial: “So voracious is its appetite and so great expectations and demand … it would work so much better if we were prepared to adopt more systematically the best practices from around the world.” The existential threat to the NHS is that its present penury is used as “proof” that Aneurin Bevan’s great free plan has failed. NHS defenders need to be eternally vigilant. And so they are.

Now the fear of more privatisation has been stirred, with the great brain of Stephen Hawking backing a judicial review to stop the creation of accountable care organisations (ACOs), a planned new configuration joining up local services into one big contract. Campaigners fear either big private finance initiatives or private equity companies could tender for these enormous area contracts or at least sweep up subcontracts. Their legal challenge claims ACOs are illegal, contrary to the 2012 act – although that’s an act they detest. They argue that any future change must be out in the open and legislated for, not slipped out with unknown consequences.

When Jeremy Hunt came under attack in the Commons over ACOs, I was more than taken aback to hear him use my name

Everything about the development of ACOs, through a welter of bamboozling acronyms, aroused the worst suspicions: done in secret without public debate, with no green paper, the organisations even have an American-derived name. It didn’t help that their inventor, NHS England (NHSE) director Simon Stevens, used to work for US company United Healthcare.

So what’s going on? Here’s the problem. Cameron’s disastrous act blew the NHS into fragments, designed to open everything up to competitive tendering. NHSE was handed this impossible system, and legally prevented from encouraging the cooperation the NHS relies on. With the service in crisis, NHSE is quietly trying to stitch the fragments back together and link up with local authority social care.

When the health secretary, Jeremy Hunt, came under attack this month in the Commons from Labour over ACOs, I was more than taken aback to hear him use my name, and that of the health thinktank the King’s Fund, when he claimed ACOs “make a massive difference to patients”. He said: “Not just the King’s Fund but Polly Toynbee and many other people are saying that.” Unlikely, since ACOs don’t as yet exist. But I called Chris Ham, chief executive of the King’s Fund, to check this out. His view, contradicting Hunt, is that ACOs should be killed off. Only Dudley and Manchester are planning them, and the legal challenge has delayed those until next year. Everything about ACOs was ill-advised from the start, he says, their secrecy and Americanised name “a lightning rod” that set privatisation fears running.

Q&A What are the financial pressures on the NHS that have built up over the last decade? Show Hide Between 2010-11 and 2016-17, health spending increased by an average of 1.2% above inflation and increases are due to continue in real terms at a similar rate until the end of this parliament. This is far below the annual inflation-proof growth rate that the NHS enjoyed before 2010 of almost 4% stretching back to the 1950s. As budgets tighten, NHS organisations have been struggling to live within their means. In the financial year 2015-16, acute trusts recorded a deficit of £2.6bn. This was reduced to £800m last year, though only after a £1.8bn bung from the Department of Health, which shows the deficit remained the same year on year. Read a full Q&A on the NHS winter crisis

The future, Ham says, is integrated care partnerships that draw together local NHS services into voluntary groupings combining hospitals, GPs, community services and local authorities. They are not compulsory, just local NHS and councils choosing to cooperate, while each remains legally responsible for its own budget.

In Wolverhampton, for example, many GPs have chosen to become directly employed by the hospital, abandoning their old small business status to work in one combined hospital and community system, as Bevan always wanted. Salford is another partnership well advanced, with the local Labour council closely involved.

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But that is an NHS system, the opposite of what Cameron’s 2012 act ordained. No wonder the private sector is up in arms at being excluded, and threatening legal action. In evidence to the Commons health select committee, NHS Partnerships, representing private companies, claims competition and “choice” are being illegally abandoned in ACOs and these other arrangements.

The private sector accuses NHSE of “introducing inflexible and unaccountable monopoly-provider models with a ‘too big to fail’ and ‘like it or lump it attitude’ to patient care”. Their members are “frustrated at being excluded” from what they see as “NHS-only discussions”. They have a point: Simon Stevens said last year that the purchaser-provider split is over.

Assailed by both privatisers and anti-privatisers, between a rock and hard place, what should NHSE do? Of course the NHS and councils should work together locally without obligatory private tendering. But that needs a change in the law, openly debated. However, it’s out of the question for this government to confess that the 2012 act was calamitous. What’s more, in Theresa May’s wobbly regime, the right would oppose abolishing private competition.

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For now, local cooperation will have to work as best it can, ducking and diving within the law. Fine for model districts like Salford, but reports from many places show huge obstacles. Without money to ease cooperation, fire-fighting hospitals can’t divert funds to the community, even if it saves them in the long run. Cash-starved silos cling to their own meagre funds. Impoverished councils have even less leeway.

Only a new act creating a rational, district-level unity of health and care services can ensure that everywhere all services pull together. But that would need a new government.

• Polly Toynbee is a Guardian columnist