She said: "The Chancellor will set out in due course before the spending review, he'll set out how the whole package of funding that we'll be putting, but it is right, I think, that we say to people that because the NHS is so important to us that we do look at asking for the country to contribute more, but in a fair and balanced way".
She added: "The Tories" claim that this is funded by a "Brexit dividend' is simply not credible as the United Kingdom will be paying a £40bn bill to leave the EU".
"We remain deeply concerned about the impact of Brexit on the NHS and need a commitment that any post-Brexit trade deals the United Kingdom enters into must not open up our NHS to privatisation or endanger public health initiatives - that simply can not and must not be allowed to happen".
On Sunday Mrs May promised that, by 2023, an extra £20bn a year will be available for the health service in England on top of any rises to keep up with inflation.
In fact, the Bank of England has calculated the United Kingdom is already around £400m a week worse off since the referendum result - more than the £350m a week the Leave campaign pledged for the NHS.
In terms of what the NHS needs in order to function, 3.4% appears to be enough to maintain business as usual: the Institute of Fiscal Studies said the service would need 3.3% in budget increases to stand still, but would need 4% for any kind of improvement to services.
British Prime Minister Theresa May.
However, it was also unclear how much of the money would be "frontloaded" and how much be only be delivered towards the end of the five-year spending plan, to start next April.
"What is becoming increasingly clear on both sides of the border is the Tories and the SNP only care about headline-grabbing figures and sticking plaster solutions, rather than a plan to fix the health service for the long term".
The trailing of the announcement has splashed every newspaper and Sunday morning political show, but it's very thin on detail - and it's not how we usually talk about NHS funding (we'd usually refer to spending each year, not every week).
There are broader problems, too: despite renaming Jeremy Hunt's role to include responsibility for social care, this announcement does little to address tackling that issue.
In a speech in London, the prime minister will stress the NHS must ensure "every penny is well spent".
"Our NHS is hugely valued by people in Scotland, but we have seen services under severe strain in recent years. But it also presents a big opportunity for the NHS to write an entirely new chapter in its history".
In reality, they would likely raise it in a different way to make it less obvious - but one way or another, this will need to be paid for: until they confirm how we'll pay for the money the NHS needs, the pledge to fund the health service will ring hollow.
The announcement, to be followed by a major speech by Ms May on Monday, marks an acceptance that the Conservatives could not go into the next general election with the NHS still in crisis.
"Labour is pledging a 5 per cent increase this year and we are being honest with how we will pay for it".
Mr Stevens said: "As the NHS turns 70, we can now face the next five years with renewed certainty".
But in a Sky News poll, 54% of nearly 72,000 voters said they would be willing to see a hike in their tax bill if it meant more funding for the NHS.
As part of the initiative, the health service will draw up a long-term plan led by doctors setting out how the resources should be best used.
"And the invitation to the NHS to develop consensus proposals for legislation will help accelerate the move to more integrated care, and ensure taxpayers" money is spent to maximum benefit'.
"I believe the best days for our NHS are ahead of it - this financial commitment by the Conservatives will let our health care professionals work to build a stronger, safer and better NHS for all of us".
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