Not a week goes by without another sign of extreme stress in the NHS. Winter is coming, as the warning goes, with 40,000 nurse vacancies unfilled, debts mounting and for the first time ever the NHS next year takes a real cut in per-capita income.

What can people do? Show political willingness to pay more tax: that comes first. But something else requires a change in public attitudes. A shocking National Audit Office (NAO) report today shows how fast the cost of medical negligence cases is rising: £60bn is set aside by trusts to cover claims – not all to be paid out in one year, but money held over. That’s a sharp rise from £51bn in the previous year, and the NAO says it’s one of the government’s biggest liabilities.

By 2020 the NHS will be paying out £3.2bn a year in claims. How much is that? Here’s the rough scale of it: every 1% extra in pay to NHS staff in England costs £500m. So, for that negligence money, they could have a hefty rise, according to the Institute for Fiscal Studies. Or the 50,000 empty NHS posts could be filled, at a cost of £2-3bn, according to the Public Accounts Committee.

Medical negligence claims have soared since the introduction of no-win-no-fee deals, as lawyers now tout for business, even advertising in NHS waiting rooms. The bonanza for lawyers has been remarkable: today’s report finds that in 61% of successful cases, the legal costs are higher than the damages paid out.

The big question is this: do we really want the NHS paying out vast sums, mostly to lawyers, when that money would be better spent on the service itself? Two babies born at the same time, in the same ward, both with cerebral palsy, both have identical needs and rights. But if one set of parents can prove medical negligence, yet the other has to accept an “act of God”, one family may get an enormous payout to help make that child’s life better, the other nothing much. High-value claims for birth injuries have risen at 9% a year for the last decade.

However much money goes into the NHS, it always was, and always will be, a rationed service. If one type of patient gets more, another gets less. Using public services is a social contract entirely different to shopping. We are all in it together, and resources need to be as fairly shared as possible between all citizens. The “slip and trip”, sue-your-council attitude undermines the idea of the collective endeavour of public services. Some 10,600 new claims were made against the NHS last year – a number that’s doubled in a decade.

Without doubt, leading lawyers in this field will fire off letters on reading this: they always do. They will cite cases of monstrous behaviour – look at the surgeon Ian Paterson, who mutilated women’s breasts for money and for fun. He is in prison, where he belongs.

But here’s another question: if the NHS – and all other public services – dealt with complaints fast and transparently, holding open enquiries, getting quickly to the cause of what went wrong, then would so many victims really need cash compensation? All people with disabilities need the same level of care and assistance, which should be far better. Some negligence money could be spent on that.

Victims of medical accidents need apologies. They need to see justice done and to know errors will be put right, with inadequate practitioners retrained or barred. Many, if not most, claimants are only driven to the courts by fury at defensive, dilatory responses to complaints where officials drag their feet hoping claims will go away. But one reason for official defensiveness is the soaring cost of insurance against claims, and insurance companies telling them to admit nothing. If fear of massive payouts from threadbare budgets were lifted, complaints could be handled faster and better.

This question will press time and again, as claims rise. Grenfell victims and thousands more users of every public service will seek damages. Who gets what will always feel unjustly random. What kind of compensation from a public service is due to whom, and why, is long overdue for public debate. It’s complicated – the sort of issue that needs a Royal Commission.

There used to be a concept of crown immunity that spelled out the special social contract between citizen and service. Is it time to return to something like it? Citizens need to ask themselves if they want ever larger sums of money drained from services to go to a few claimants who can prove their case, while a great many lawyers make more than the value of the original claims: the public realm belongs to us all, equally.

• Polly Toynbee is a Guardian columnist