In The Times yesterday, the commentator and confidant of the chancellor, Danny Finkelstein, penned an intriguing article calling for a new 'NHS tax'.

It merited attention not because it called for an hypothecated tax for the NHS - an idea that appears with predictable regularity in policy debates - but because it was framed as the solution to a pressing problem faced by Conservative strategists: how do they continue to demonstrate their fidelity to the NHS while constraining the upward pressure it places on the public finances, and forcing open political choices about the scope of its services and its efficiency?

The NHS absorbs about a third of all departmental spending. Insulating it from real-terms cuts - alongside schools and aid expenditure - places significant pressure on unprotected services such as the police, social care and post-16 education. But historically the NHS has had average annual real terms spending increases of 4 per cent, so a sustained period of what Whitehall calls 'flat real' settlements - that is, spending that only increases with inflation - is unprecedented. It also faces significant increases in demand imposed by an ageing society, technological change and the spread of chronic conditions. All of this means that the 'protection' of the NHS in the next parliament will be largely illusory if it continues to receive only inflation-indexed budgets.

It is not possible to spring this trap simply by cutting social security spending. Regardless of the justice or otherwise of cutting tax credits, housing benefit and other welfare entitlements of the working-age poor, taking £12 billion out of the social security budget a year in the next parliament still leaves departmental spending facing cuts of 2.3 per cent per annum. Keeping in place the 'protections' for the NHS, schools and aid spending means that the cuts to unprotected departments rise to 7 per cent a year. Respected analysts at the IFS believe that to be completely untenable. They are right.

That is why tax rises after the next election are inevitable. Nick Clegg committed himself to this position in his sharp rejoinder to Osborne's statement. He now wants 25 per cent of the deficit reduction in the next parliament to be achieved by tax increases, which implies raising an extra £6 billion in revenues. A 'mansion tax' raises about £2 billion a year, so other taxes will be needed to plug the gap. Unfortunately, the Liberal Democrats also want to slash revenues by increasing the personal tax allowance to £12,500, which will cost a lot more than the £6 billion they are seeking to raise in wealth taxes. So they have got themselves into a fiscally confused, if not incontinent position.

This is where the NHS tax proposed by Finkelstein and raised in a report IPPR published earlier this week comes in. If there is one thing the public supports increased taxes for it is the NHS. Despite continued efforts to dislodge them from their loyalty to the NHS, the British public remain resolutely supportive of it. So, if we want to be honest about the need for tax rises after the next election and to ensure that our health services are properly funded without placing untenable pressures on other services, a new NHS tax merits public consideration.

Ideally, it would be linked to increases in longevity in a structured way, rather as has become the case for increases in the basic state pension age. The OBR could project, based on known demographic trends, the level of spending that would be required over the next 20 years to deal with the demand on the NHS that will result from increased numbers of old people, while also maintaining the level of service to the rest of the population and requiring productivity improvements.

Efficient funding of the NHS will require reforms that go beyond its current boundaries, however. Finkelstein is right that doing nothing is not an option, and that we should want to make NHS costs more transparent, focus minds on its levels of productivity and drive down the costs of expensive hospital stays. But these goals can only be achieved by integrating health and social care, while planning the NHS alongside other community services. As more and more people live for decades with long-term conditions like diabetes and heart disease, the vast majority of their treatment is self-care at home. Any new NHS tax should therefore be considered in the context of the introduction of long-term locally integrated budgets for health and social care services, along the lines of the arguments advanced by Andy Burnham for 'whole person care'.

Indeed, the argument for an NHS tax offers the intriguing prospect not just of placing the health service and the wider public finances on a more sustainable footing but of cracking the hitherto intractable problem of funding care of the elderly. Back in 2001, when Gordon Brown responded to the Wanless report into NHS funding by increasing national insurance, he considered expanding the scope of the reform to cover social care too, but drew back. In the future, however, it will be imperative to integrate the financing of the NHS and social care. An NHS tax may be the best way of mustering public support for tackling two major public policy challenges in one go.