Mr Hunt promised he would "come forward" with a "long-term plan" for the social care system.
The prime minister has so far refused to be drawn on whether increased taxes and higher borrowing will be needed to allow for the £20bn increase to the health budget in real terms (accounting for inflation) by 2024, but will use the keynote address in the capital to explain why the NHS does need greater funding.
The prime minister said this will be partly funded by a "Brexit dividend" - money Britain will supposedly save from no longer contributing to the European Union's budget. "By the end of the meeting, some sources of funding had been more heavily pencilled in than others", a ministerial source said.
Economist Paul Johnson, the head of the Institute for Fiscal Studies, said the "divorce bill", plus commitments to replace funding in key areas, would swallow up all of the returning European Union contributions until 2022.
Pointing to the success of Conservative austerity policies, she added: "We are now bringing down debt as a proportion of GDP, we have these fiscal rules in place and we are sticking to them, and now is the time to look at our spending priorities".
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The government hasn't confirmed how the budget increase is to be funded, but speaking to BBC Breakfast, health secretary Jeremy Hunt said more information would be announced in the budget.
"When we leave we won't be doing that".
"I want to make sure that as see as we see this £2 billion in additional money coming to Scotland that those who work in our health service, who have been telling us that they need this key investment, will see this money coming through".
Asked if he believed the "Brexit dividend" would deliver enough money, Mr Stevens told MPs: "Both the Prime Minister and the Chancellor are crystal clear that this money will be available to the National Health Service over the next five years".
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.
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She noted: "I'm one of those people who have had their lives saved by the NHS".
Mrs May is using her speech in London to say the NHS has a special place in British life, hailing the work of those who treated victims of the Manchester Arena attack previous year.
She also said there may be a reform of health service regulation, including the internal market for commissioning treatment, which have been criticised by NHS leaders.
Earlier this year, Chancellor Phillip Hammond warned that public spending could not increase because Britain's economy was suffering due to uncertainty over Brexit.
In a speech in London, the prime minister will stress the NHS must ensure "every penny is well spent". "It must be a plan that tackles waste, reduces bureaucracy and eliminates unacceptable variation, with all these efficiency savings reinvested back into patient care".
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"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".