Writing exclusively for HuffPost UK, 12 high-profile clinicians, including ex-chair of the Royal College of GPs, Dr Clare Gerada, slam the Prime Minister's big NHS announcement and say "there is in fact a growing Brexit deficit" in the health service.
However speaking to the Today programme this morning, Hunt admitted the Brexit dividend "alone won't be anything like enough".
Taxpayers will have to pay more to help fund a £20bn boost to the NHS, Theresa May has confirmed.
The NHS has been struggling to cope with funding shortages in recent years, particularly during the flu-ridden winter months.
Answering questions afterwards the prime minister said greater tax revenues would be part of the answer.
"An average 3.4 per cent increase in NHS funding would be welcome but historically unremarkable, a little less than the long-run trend of 3.7 per cent", said Tom Kibasi, director of the IPPR think tank.
NHS spending will rise by around 3.4% a year in inflation-adjusted terms over the next five years to hit the target.
The announcement is timed to mark the 70th anniversary of the NHS, which delivers free access to care for everyone living in Britain.
Health Secrtary Jeremy Hunt said: "As the Prime Minister announces a historic long-term funding boost and 10-year plan for the health service, we are backing the NHS to show the world what a cutting-edge 21st century healthcare system can look like too".
"There is no Brexit dividend and an NHS funding plan that relies on such a source would be literally worthless".
"They've told us they're going to pay for it from a Brexit dividend".
"We will listen to views about how we do this and the chancellor will set out the detail in due course", she said.
She also intimated that there would be rises in income tax to help fund additional resources, as she said "we as a country will contribute a bit more".
Director of the Institute for Fiscal Studies, Paul Johnson, also said the so-called windfall from European Union withdrawal would not materialise when the United Kingdom stopped paying more than £9 billion a year to Brussels due to the "divorce bill" of some £39 billion, and other economic factors.
The newspaper said the precise details of how the spending increase would be funded would be disclosed in a future government budget.
He said the financial settlement with the EU, plus the UK's commitments to replace EU funding, "already uses up all of our EU contributions" for the next few years.
"I'm one of those people that have relied on the NHS throughout their entire life". "She won't stand up to vested interests and is instead asking patients to rely on a hypothetical Brexit dividend". And I'm very clear that we need to make sure that in dealing with social care it doesn't put added pressure is on to the NHS.
There isn't any extra guaranteed money available as a result of ending our payments to the European Union budget, because those savings are likely to be more than offset by other costs associated with Brexit.
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