Mrs May said the money, which would not be used for social care, would amount to an increase of 3.4pc, and said the country would also have to "contribute a bit more" to health service funding.
The Association of the British Pharmaceutical Industry's chief executive Mike Thompson said the funding announcement for the NHS is "very much welcome".
The PM has just announced a grand new plan to invest in the National Health Service.
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.
"We are absolutely confident that we will deliver a Brexit deal that will.be good for the United Kingdom, good for our European friends and partners".
May said in a speech that the cash-strapped National Health Service would receive 20.5 billion pounds ($27 billion) in extra funding by 2023-24, a 3.4 percent annual rise in real terms.
"The Prime Minister should apologise for misleading people about NHS funding and instead level with the public about the need to increase taxes to pay for a better NHS".
"If you look at the arrangement we've come to with the European Union in terms of paying our exit bill - and you add to that the commitment the Government's already made to keep funding farmers and so on - there is literally arithmetically no money".
The prime minister is facing a backlash for linking her NHS cash boost with the Vote Leave pledge during the referendum campaign to spend Britain's European Union contributions on the health service instead.
Mr Hunt acknowledged that the extra cash for the NHS will not cover social care, but said a long-term plan was being prepared on the issue.
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The announcement is timed to mark the 70th anniversary of the NHS, which delivers free access to care for everyone living in Britain.
"The truth is that in spite of this welcome extra investment we will face hard choices and we need an honest debate about what the NHS can and cannot do", he said.
"Increases of at least 4% a year are the minimum needed to tackle the backlog of financial problems from eight years of austerity".
We've written before about the concerns raised by think tanks and NHS senior managers that funding specifically targeted at the NHS has come at the same time as other elements of health spending, for example public health, have been falling.
She attacked the Cameron government's key health reform - driven through by the former Health Secretary, Lord Lansley - which created clinical commissioning groups to negotiate legal contracts with other parts of the NHS.
She noted: "I'm one of those people who have had their lives saved by the NHS".
Speaking on the BBC's Andrew Marr Show yesterday morning, Ms May said the Government will draw up a 10-year plan for the NHS, which will include "more doctors, more nurses" and "significantly more money going in to the NHS".
"I'll be making sure we keep the pressure on the SNP to deliver for Scotland and deliver for our NHS".
"We will listen to views about how we do this and the chancellor will set out the detail in due course", she said. We certainly haven't seen that.