TAX rises to pay for a £20.5 billion-a-year boost to the NHS budget will be "fair and balanced," Theresa May has vowed as she called on Nicola Sturgeon to use Scotland’s near £2bn knock-on windfall to fund health care north of the border.

The Prime Minister insisted the NHS was now the UK Government’s “number one spending priority”.

She explained UK ministers would take a "responsible" approach to the plan for extra spending, which would see an additional £394 million a week going to the NHS south of the border in 2023/24.

Mrs May repeated her claim that part of the increase would be funded by a "Brexit dividend"; a suggestion widely attacked as unrealistic by political opponents and even some Conservatives.

In a keynote speech in London, Mrs May acknowledged that "despite more funding, more doctors and more nurses, and great progress on treatments, our NHS is under strain" as it coped with an ageing population and changing health challenges.

"We cannot continue to put a sticking plaster on the NHS budget each year," she declared. "So we will do more than simply give the NHS a one-off injection of cash.

"Under our plan, NHS funding will grow on average by 3.4 per cent in real terms each year from 2019/20 to 2023/24.

"We will also provide an additional £1.25bn each year to cover a specific pensions pressure.

"By 2023/24 the NHS England budget will increase by £20.5 billion in real terms compared with today. That means it will be £394m a week higher in real terms.

"So,” she explained, “the NHS will be growing significantly faster than the economy as a whole, reflecting the fact that the NHS is this Government's number one spending priority."

The PM made clear that the £1.8bn consequent windfall for Scotland from the £20bn cash boost across England should also be spent on financing health care in Scottish hospitals and GP surgeries.

“Because the UK Government is increasing NHS spending in England, extra money will go to Scotland, Wales and Northern Ireland under the Barnett Formula, which ensures every part of the UK gets a fair share of public spending.

“While it is up to the devolved administrations to spend the money as they see fit, I believe everyone in the UK should benefit from this extra funding for the NHS.

“So I urge the devolved administrations in Scotland and Wales to use this money to improve the NHS and to develop their own long-term plans for NHS Scotland and NHS Wales. This way the vision I have set out today can benefit the whole United Kingdom,” insisted Mrs May.

Shona Robison, the Scottish Government’s Health Secretary, has made clear that in the past any consequentials from increased spending in England have always gone on health care in Scotland.

In her speech, the PM conspicuously failed to reveal how all the money would be raised but said: "Some of the extra funding I am promising today will come from using the money we will no longer spend on our annual membership subscription to the European Union after we have left."

But she added that the scale of the Government's ambition went beyond that: "So across the nation, taxpayers will have to contribute a bit more in a fair and balanced way to support the NHS we all use."

Her Tory colleague, Sarah Wollaston, who chairs the Commons Health Committee, branded talk of a Brexit bonanza "tosh", while Labour’s John McDonnell said the Government's plans were "just not credible" without details of how they would be funded.

Paul Johnson, the Director of the respected economic think-tank, the Institute for Fiscal Studies[IFS], also said the so-called windfall from EU withdrawal would not materialise when the UK stopped paying more than £9bn a year to Brussels due to the "divorce bill" of some £39bn and other economic factors.

Jeremy Hunt, the UK Health Secretary, indicated that separate plans being drawn up to increase funding for social care could include measures to encourage people to save more to cover needs in their old age.

He said ministers "happen not to agree with the IFS’s views", even though they are based on the projections of the Government's own independent forecaster, the Office for Budget Responsibility.

Mr Hunt revealed how "huge, very difficult" discussions with the Treasury "went to the wire" until Philip Hammond, the Chancellor, was certain that the additional spending was affordable.

"We are clear that there will be an increased burden of taxation," he confirmed.

But he said the funding details would be held back until Mr Hammond's Budget in November to give the NHS time to say how it would spend the money.

"We will be able to explain exactly where every penny is coming from but we will do that in the Budget," stressed the Secretary of State.

"Why are we not doing it now? We do know - the Treasury has done its sums, it hasn't made its final decisions but it is very clear - this can be affordable.

"The reason why we are not spelling it out now is because we want to give the NHS six months to come up with a really good 10-year plan.

"When we have that plan in November, we will say: 'This is a great plan, we accept that it is going to lead to improvements in cancer care and mental health and so on.'"

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.