The announcement marks a significant victory for Hunt, who has been lobbying Philip Hammond, the Chancellor, for a significant funding boost for the NHS, as well as Brexiteers such as Boris Johnson, who urged May to deliver on their campaign promise. Critics say taxes and borrowing will have to rise in order to deliver the pledge, but no detail on how it will be paid for is expected before November's budget.
He said: "Everyone who wants to see the NHS's funding put on a sustainable basis will be alarmed that the Prime Minister thinks it can be paid for out of something that doesn't exist".
Royal College of Midwives chief executive Gill Walton said talk of a Brexit dividend was "misleading in the extreme" because "Brexit will cost us money, not save us anything". But it's right that we must recognise the impact social care has on the NHS, and the way in which these work together.
The prime minister said this would be funded in part by a "Brexit dividend", but also hinted that there could be tax rises too.
She told Andrew Marr on Sunday morning: "What we're doing is saying very clearly as a government that the NHS is our priority".
In an interview with Tom Swarbrick, May's ex-head of broadcasting in Downing street on LBC radio station, the prime minister announced that the the United Kingdom will be able to spend "around £600 million a week" more on the NHS by 2024, in what ministers are calling a "70th birthday present".
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Today Theresa May will formally announce a new 10-year NHS funding plan already trailed over the weekend.
May's speech evoked a discredited claim by the pro-Brexit campaign in Britain's 2016 European Union membership referendum that leaving would save the country 350 million pounds a week, and that the money could be spent on health care instead.
He added: "If they've [the government] got a good case to make on NHS reform, then make it, but why pull in all this divisive stuff?"
Mr Hunt said the announcement was "bold and ambitious", adding: "Some of the new investment in the NHS will be paid for by us no longer having to send annual membership subscriptions to the European Union after we have left".
An analysis by The Health Foundation, an independent charity committed to bringing about better health and healthcare in the United Kingdom, warned that a 3.4% annual rise would be insufficient to prevent patients having to wait even longer for care. That bit would need to reach an additional 1,200 to 2,000 pounds per household a year by 2033 to 2034, according to the IFS.
Analysis by the Resolution Foundation think tank found that freezing the personal tax allowance, higher rate threshold and personal National Insurance threshold might raise around £4 billion. It has been estimated that the measure could raise nearly £4 billion by the end of this Parliament.
Penrose, a former Cabinet Office minister, urged Hammond to introduce a new "fiscal rule" to ensure "we only live within our means".