With no extra money available to resource a “seven-day health service” properly, the health secretary, Jeremy Hunt, can only attempt to achieve this reform by stretching existing resources across seven days rather than five. Without more money, this means worsening doctors’ conditions of work. The doctors, whose union Hunt labelled “totally irresponsible”, have spotted this.

So the fundamental cause of the threatened doctors’ strike, as so often, is the underfunding of the NHS. Which points up an urgent question: how can we break through the current constraints to a properly resourced health service, offering good working conditions as well as excellent care? The question is pressing because the financial squeeze continues to tighten.

The facts are uncontroversial. The annual rise in overall health spending since 2010 averaged 0.8%, compared with an increase in demand and cost pressures associated with an ageing population of between 4% and 5%. After years of stringent economies, health providers finally came to the end of the line and have sunk into deficit, forced to cut services. So far, so familiar.

Less well appreciated is that, following November’s comprehensive spending review, the outlook for this parliament is for more of the same. The famous Conservative election pledge of “£8bn extra for the NHS” amounts to an annual rise in real terms of less than 1%. This reality was disguised by “frontloading” £3.6bn of the £8bn for 2016-17, so creating some leeway. But the total commitment is unchanged, so the increases earmarked for later years are tiny. The underfunding will go on, bringing with it a further erosion of standards.

Must we accept this? When, in a recent report, the OECD ranks the UK 20th of 23 countries for cancer survival, 19th of 31 for stroke, and 20th of 32 for heart attack deaths, it is critical not just to maintain but to improve standards of care. But why should we imagine that we can match standards achieved by countries such as Germany, France, Switzerland and the Netherlands if our government aims to spend 7% of GDP on healthcare when theirs spend 11%? The OECD calculates that, simply to match standards in similar countries, the NHS needs 75,000 extra doctors and nurses (which would have avoided the dispute). Where can the extra money come from?

One possibility is higher taxes or national insurance, but in the longer term this would present difficulties not generally appreciated. Historically, NHS spending has grown more rapidly than GDP. Over the past 30 years its share of GDP has increased by more than 2.5%, but this has been financed without a rise in taxes because defence spending has declined by a similar amount.

But the fall in defence spending has come to an end. So if health spending has to rise faster than GDP to keep pace with demographic pressures, this can only be achieved under the present financing system if there is not just a one-off but a continuing rise in taxes indefinitely. The tax and spend picture has fundamentally changed.

An obvious conclusion follows: if we want standards of healthcare comparable to similar countries, and if at the same time the prospect of continuing tax increases is unacceptable, we must be prepared to contemplate income for the NHS from other sources.

Mainland Europe provides different models illustrating how this can be done. In France, mainstream healthcare is mainly financed from public funds, but the proportion of treatment costs covered varies depending on the service provided. Costs not covered are funded by complementary private insurance, which 90% of the population takes out. The other 10%, on low incomes or with chronic conditions, are paid for from special schemes, so that everyone receives the treatment they need.

In Switzerland and the Netherlands, health insurance is required by statute, with insurance companies obliged to cover a basic package of services at a price set by the government. People purchase complementary insurance to pay for costs or treatments not covered.

A complementary insurance system in Britain, based on the French model, could in time provide additional funds financing, say, a quarter of NHS activities, which would go a long way to closing the financing gap with similar countries and enable us to maintain international standards.

But in order to tackle the problems the health service faces, we have to ditch the ideology. The NHS needs more money. To those prejudiced against insurance in any form, who say “where insurance is involved the poor will suffer”, I say: look at those European countries. In every case there is universal access to healthcare, with special provision for those with special needs. No one need suffer.

To those committed to the “free at the point of use” mantra, I say that, in a country five times richer than in 1948, we can adopt an alternative principle: “No one should be denied the healthcare they need for financial reasons.”

Why not have a system in which those who can make affordable contributions to the cost of their care do so, while those who cannot are provided for. How else will we save the NHS?

• Christopher Smallwood will be speaking at a Guardian Live event, How do we pay for the NHS we want?, on Wednesday 10 February. Details at membership.theguardian.com/events