“The NHS does not need more money; it needs more reform,” Theresa May told a recent meeting in Downing Street. May’s mantra on public services was forged at the Home Office, where crime fell despite her reducing the number of police officers – although the drop was in line with international trends.

So May’s instinct, as shown at Prime Minister’s Questions today, was to point to differing performance levels locally and play down the mountain of evidence growing daily about the pressures on hospital wards, accident and emergency units, GPs, mental health services and social care. You can pass the parcel from one part of the system to another for a while – most damagingly, social care cuts have put huge strain on hospitals through extra admissions and bed-blocking – but eventually the whole system creaks. What we have now is not just another winter crisis; it is systemic.

That is clear from a coalition of 75 organisations working in the health and care sector, who argue in an open letter to May for a cross-party review to find a long-term solution to the funding problems. Their call has been backed by 20 MPs from across the political spectrum, led by Norman Lamb, the Liberal Democrat former health minister, who is steering his party towards backing a 1p rise in tax or national insurance with the proceeds ring-fenced for health and social care.

May should take this escape route while it is still there. She agreed to meet Lamb to discuss it but has already asked the Cabinet Office to seek a long-term solution for social care, and may spurn a search for an all-party consensus. She may live to regret it.

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In November, the Government tried to pass the buck to local authorities by again allowing them to raise the council tax to fund care, but it is not working. County councils in England are wary of a tax hike on the eve of their elections in May. The electoral cycle is more favourable for May; if she raised a dedicated health and care tax now, it would probably be forgotten by the 2020 election. It might even prove popular, as it was when the then Chancellor Gordon Brown did it in 2002. The obvious solution would be to target the money on social care to relieve the pressures on hospitals, and give the NHS and councils financial incentives to integrate their services.

Jeremy Hunt, the Health Secretary, is in the eye of the storm and seems more open-minded than Downing Street. He told the Commons on Monday: “I just wonder if we don’t need to start an honest discussion with the people about how we are going to devote more resources to health in this country.” Such a debate would be welcome. It might even lead May away from her “more reform, not money” stance. She might realise that her vision of a “shared society” and “active government” will not run on thin air and will need money. May’s decision to dump George Osborne’s plan to run a budget surplus by 2019-20 was right because of the Brexit vote but has raised false hopes that the age of austerity is over. It is not.

Government spending as a share of GDP is projected to fall to its lowest post-war level (about 36 per cent) by 2019-20. Demographic pressures, such as one million more over-65s in next five years, will raise the cost of health, social care and state pensions. The gap between forecast spending and tax receipts could rise to £341bn by 2050, according to the IPPR think tank. No amount of “reform” will bridge that gap.

Team May’s instinct, it seems, is to shoot the messenger – whether Sir Ivan Rogers, our departed ambassador to the EU, or Simon Stevens, the widely respected chief executive of NHS England, who appears to be the victim of a blame game as the NHS pressures mount.

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Stevens is not a soft target like Rogers, who could be accused (unfairly, in my view) of not accepting the referendum result. While the public is divided over the EU, Stevens is the champion and figurehead of the country’s most popular institution.