Taxpayers are to be asked to help fund a £20bn a year injection of extra cash into the National Health Service by 2023-24 that will pay for thousands more doctors and nurses, while cutting cancer deaths and improving mental health services, Theresa May will say today.

The announcement, before the NHS’s 70th birthday next month, will represent the biggest funding boost since Gordon Brown imposed a one percentage point rise in National Insurance to pay for more NHS spending in his 2002 budget, in the face of Tory claims that Labour was slapping a “tax on ordinary families”.

Government sources said the increases, which would be paid for in part by a “Brexit dividend”, would amount to around £600m a week extra for the NHS in cash terms within six years.

Health and social care secretary Jeremy Hunt said last night that the government wanted to “show the world what a cutting-edge 21st-century healthcare system can look like”.

He added: “This long-term plan and historic funding boost is a fitting birthday present for our most loved institution. Like no other organisation could ever hope to be, the NHS is there for every family at the best and worst of times, from the wonder of birth to the devastation of death, living and breathing those very British values of decency, fairness and compassion.

Quick guide Is there a Brexit dividend? Show Hide What is a Brexit dividend? Britain contributes more money to the European Union than it takes out. Vote leave campaigners emphasised before the referendum that leaving the EU would free up these funds for the UK government to spend on vital infrastructure and austerity-hit services like the NHS. Is there a Brexit dividend? The Office for Budget Responsibility (OBR), which is the Treasury’s independent economic forecaster, has calculated that any benefit to the UK has all but disappeared in the past two years, largely due to a slowdown in the economy that it blames on the Brexit effect. What is the Brexit effect? Once it became clear to businesses and consumers that the government was split over how to negotiate Britain’s departure from the EU, creating huge uncertainty about the outcome, investment fell, productivity stagnated and consumer spending flatlined. This has forced the OBR and the other main forecaster, the Bank of England (BoE), to downgrade GDP growth this year and next year. The implied hit to the public finances is about £15bn a year by the early 2020s. Has all the dividend gone? Britain pays around £19bn into the EU pot each year, much of it coming back to the UK in the form of subsidies for farmers, research and development and infrastructure projects plus a £5bn rebate. This situation will continue during a transition deal, denying the government the Brexit dividend until 2020. What about after the transition period? The OBR said the UK’s £5bn rebate has already been “spent” ​on domestic priorities and cannot be spent again. The Institute for Fiscal Studies said in its assessment that the remaining £14bn could theoretically be redirected, but the government has already pledged to replace at least some EU spending (for example, farming subsidies) for some years, leaving an £8bn surplus. However, a reduction in GDP of just 1% translates to a fall in tax revenue of more than £8bn. How much has GDP growth fallen? The Bank of England said the trend rate of growth for the UK has fallen from around 2.5% to 1.5%, which matches the fall needed to wipe out the Brexit dividend. BoE governor Mark Carney said household incomes after adjusting for inflation were £900 lower than expected before the referendum vote. “Real household incomes are about £900 per household lower than we forecast in May of 2016, which is a lot of money,” he said, referring to the total lost growth for incomes in the two years since the 2016 referendum.

By Phillip Inman

He said the extra cash “recognises the superhuman efforts made by staff over the last few years to maintain services in the face of rapidly growing demand. But it also presents a big opportunity for the NHS to write an entirely new chapter in its history”.

Details of how the public will be required to pay through tax rises, and the proportion of the funding increases they will pay for, will not be spelled out until the budget, because of ongoing arguments involving the chancellor Philip Hammond, Hunt, and No 10.

It is understood that a freeze on tax thresholds is being considered as one option to pay for up to £10bn of the extra annual cash injection. This would, however, mean another big policy U-turn by the Tories, who are committed to raising the tax-free threshold to £12,500 and increasing the level at which people pay high-rate tax to £50,000 by April 2020.

May is expected to say that the rest of the package will be paid for from extra borrowing within the government’s fiscal limits and, controversially, from a “Brexit dividend” resulting from the UK’s exit from the EU in March 2019. Claims by the official VoteLeave campaign that £350m a week extra could be spent on the NHS if the British people voted to leave were hotly contested during the EU referendum campaign in 2016, with critics saying that the economic damage of Brexit and resulting loss of government income would far outweigh any Brexit dividend.

The independent Health Foundation cast doubt on whether the cash would be enough, suggesting any increase that fell significantly below the 4% extra a year that had been demanded by Hunt would not lead to improvements.

Anita Charlesworth, the charity’s director of research and economics, said: “Increases of 4% a year above inflation are the minimum needed to allow the NHS to improve and modernise. Without funding growth at this higher level it is hard to see how there can be any improvements in mental health and cancer care. And if funding growth is limited to the NHS England element of the health budget, this will mean ongoing and severe problems in public health and staffing – with no end in sight to the serious shortages of nurses and GPs. There are potentially really tough times ahead for the health service.”

May’s announcement follows months of intense debate at the top of government about how to prepare the NHS for the challenges of an ageing population and the rising costs of care and drugs, which have taken NHS finances to breaking point. NHS England will be asked to come up with a 10-year plan laying out how it will use the extra money to provide more doctors and nurses and improve all key services.

Last night, some Remain-supporting Tory MPs said the timing and content of the announcement was “cynical” and designed to give a misleading impression that Brexit would make the country better able to fund public services.

With more key parliamentary battles over the Brexit withdrawal bill expected this week the rebels believe May is trying to sell Brexit as a money-spinning course for the country to take, when they say the reality is that is loaded with economic risk. One senior Tory said it was “sickening” and “pathetic” that the government could claim Brexit would provide extra money for the NHS when the reverse would be the case.

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In 2016, the UK government paid £13.9bn to the EU budget, according to the Office for National Statistics, and the EU funded projects and other spending in this country amounting to £4.4bn. But many economists argue that the cost of Brexit, in terms of loss of economic activity and therefore revenue to the Treasury, will far outweigh any budgetary gain from leaving.

Theresa May will spell out her plans on television interviews before explaining the changes to NHS staff in a major speech in London on Monday.

Government sources defended their record on the NHS, saying funding had increased every year since the party came to power in 2010. But they said it now urgently needed more to meet rising demand caused by people living longer, and the cost of more complex and effective treatments for patients with complex conditions.

They said a key aim was to improve cancer survival rates, improve mental health care, and expand the number of doctors and nurses in areas of most demand. They added that the plans would also involve a fresh assault on waste and inefficiency within the NHS.