I am afraid Professor Stephen Hawking, writing in the Guardian, is once again wrong in his characterisation of government policy towards the NHS.

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He does not deny that it has record funding or record numbers of doctors and nurses, but describes these as a “distraction”. Such figures surely are crucial evidence if he is arguing, as he did last weekend in a speech at the Royal Society of Medicine, that the direction of the NHS is heading towards a US-style insurance system. Such systems – which he seems to now concede are not government policy – rely on individuals, and not the state, paying for their healthcare. If that was the direction of travel, the state would be spending less, not more, on the NHS.

Likewise, more individuals would be taking out private medical insurance – again, the opposite is the case. Although there was indeed a small rise last year, overall there has been a dramatic drop in private medical insurance since 2009.

Professor Hawking’s suggestion that the NHS adopting accountable care organisation models in some parts of the country is a step towards an insurance-based system is also incorrect. On the contrary, in many ways these models weaken the “internal market”, or purchaser-provider split, to allow integrated and joined-up care. We want to encourage this because it will improve the quality of care, meaning less resources are used up in complex contract negotiations. But this has absolutely nothing to do with the funding model of the NHS, which will remain a single–payer taxpayer-funded system free at the point of use – and should do forever as far as I’m concerned.

I have said many times that I don’t believe staff have ever worked harder. We are doing all we can to support them

I do not accept his comments about the misuse of statistics, although inevitably in the heat of an industrial relations dispute there will be many such accusations hurled from both sides. To decide that one piece of research is the most credible is not “cherrypicking”, as Hawking suggested – it is doing what you have to do when researchers disagree.

But regardless of which research you back, none of us can bury our heads in the sand on the issues surrounding weekend care in hospitals. Most doctors in their hearts would rather a loved one was admitted mid-week than at the weekend. Let’s remember that the drive towards better standards of care across the week came not from politicians but from clinicians, led by the Academy of Medical Royal Colleges. To ignore their findings would be a betrayal of duty by a health secretary. Government policy is simply to make sure that four clinical seven-day standards, set by the Royal Colleges and ensuring patient access to consultants and diagnostic tests, are properly met.

Finally, Professor Hawking suggests that I think everything is working well in the NHS. On the contrary, I have acknowledged time and again the great pressures doctors and nurses are under as we face up to the need for higher standards of safety and quality alongside the challenges of an ageing population. I have said many times that I don’t believe frontline staff have ever worked harder. We are doing all we can to support them with extra funding and extra clinicians. I believe we need still more staff to deliver the highest standards of care and reduce burnout pressures – and although it will take some time to feed through, last year’s decision to expand medical school places by 25% will make a big difference.

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At the same time, we should recognise that despite pressures, staff have made real progress towards safety and quality with one of the lowest MRSA rates we have ever had, the four main hospital harms (pressure ulcers, falls, VTEs and UTIs) down 8% over three years and a transformed approach towards openness and transparency when things go wrong. They are doing a brilliant job in highly challenging circumstances.

I admire and respect Stephen Hawking, and have offered to meet him to discuss these issues further, because I believe – whatever our disagreements – that we both believe in the NHS, and share a passion that it should be the safest and best healthcare system in the world.

• Jeremy Hunt is secretary of state for health