The secretary of state for health, Jeremy Hunt, has challenged me on Twitter and in an article for the Sunday Telegraph over a talk I gave recently to the Royal Society of Medicine in defence of the NHS. Having been accused by Hunt of spreading “pernicious falsehoods”, I feel the need to respond.

Hunt doesn’t deny that he dismissed research contradicting his claim of excess deaths due to poorer hospital care and staffing at the weekend. He admits he relied on one paper by Professor Nick Freemantle and colleagues. But even if one accepts its disputed findings, the authors explicitly warn that “to assume these excess deaths are avoidable would be rash and misleading”. The editor-in-chief of the British Medical Journal, Fiona Godlee, wrote to Hunt to reprimand him for publicly misrepresenting the Freemantle et al paper. As a patient who has spent a lot of time in hospital, I would welcome improved services at the weekend. For this, we need a scientific assessment of the benefits of a seven-day service and of the resources required, not misrepresentation of research.

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Hunt’s statement that funding and the number of doctors and nurses are at an all-time high is a distraction. Record funding is not the same thing as adequate funding. There is overwhelming evidence that NHS funding and the numbers of doctors and nurses are inadequate, and it is getting worse. The NHS had a £2.4bn shortfall in funding in 2015-16, bigger than ever before. NHS spending per person will go down in 2018-19. According to the Red Cross, the NHS is facing a humanitarian crisis. There is a staff recruitment crisis. The BBC reported that on 1 December 2015 there were 23,443 nursing vacancies, and a 50% increase in vacancies from 2013 to 2015. The Guardian reported in May that the number of nursing vacancies had risen further to 40,000. There are increasing numbers of doctor vacancies and increasing waiting times for GP appointments, treatment and surgery.

Hunt misquoted me, saying that I claimed the government wants a US-style insurance system. What I said was that the direction is towards a US-style insurance system, run by private companies. The increasing involvement of private health companies in the NHS is evidence for this. Hunt chose to highlight – dare I say, cherry-pick – the fact that private companies’ share of NHS contracts rose 0.1% over the last year. This is an anomaly among the data since 2006. The NHS private providers’ share was 2.8% in 2006-7 and rose steadily to 7.6% in 2015/16. The amount of private health insurance has fallen since 2009 as Hunt said, but that is because of the financial crash. We can conclude nothing about health policy from this and in any case, it is now increasing again. As waiting times increase, private companies report an increase in self-pay where patients pay directly for care such as hip and knee replacements.

Further evidence that the direction is towards a US-style system is that the NHS in England is undergoing a complete reorganisation into 44 regions with the aim of each being run as an “accountable care organisation” (Aco). An Aco is a variant of a type of US system called a health maintenance organisation in which all services are provided in a network of hospitals and clinics all run by the HMO company. It is reasonable to expect the powerful US HMO companies such as Kaiser Permanente and UnitedHealth will be bidding for the huge contracts to run these ACOs when they go out to international tender. Hunt referenced Kaiser Permanente as a model for the future budgetary arrangements in the NHS at the Commons health select committee in May 2016.

The NHS is political, but not necessarily party political. I am a Labour supporter but acknowledge that privatisation increased under Labour governments in the past. The question is whether democracy can prevail and the public can make its demands for proper funding and public provision undeniable by any government.

• Stephen Hawking, the author of A Brief History of Time, is director of research at the Centre for Theoretical Cosmology at the University of Cambridge, where he was Lucasian professor of mathematics