Theresa May’s promise of £400m extra in weekly NHS spending within five years has been overshadowed by scepticism among experts and her own backbenchers over her claim it can be financed through a windfall delivered by Brexit.

Ahead of a major speech by the prime minister in which she will pledge a £20bn annual real-terms NHS funding increase by 2023-24, May was ridiculed for arguing that some of the money would come from a so-called Brexit dividend.

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

“At the moment, as a member of the European Union, every year we spend significant amounts of money on our subscription, if you like, to the EU,” she said in an interview on BBC One’s Andrew Marr show. “When we leave we won’t be doing that. It’s right that we use that money to spend on our priorities, and the NHS is our number-one priority.”

The Institute for Fiscal Studies (IFS) said, however, that even the government had accepted the idea of an immediate post-Brexit boost to coffers would not happen. Two senior Tory MPs who are also doctors similarly criticised the proposal.

Why claims of Brexit dividend for NHS will raise Remainers’ anger Read more

Sarah Wollaston, who chairs the Commons health and social care committee, tweeted:

Sarah Wollaston MP (@sarahwollaston) The Brexit dividend tosh was expected but treats the public as fools. Sad to see Govt slide to populist arguments rather than evidence on such an important issue. This will make it harder to have a rational debate about the ‘who & how’ of funding & sharing this fairly.

Dr Phillip Lee tweeted:

Dr Phillip Lee MP (@DrPhillipLeeMP) As a GP, I‘m happy to see more money for our health & social care. We need to spend more as our population ages. But we must be honest about how we are going to pay. There is no evidence yet that there will be a “Brexit dividend” - so it’s tax rises, more borrowing or both

The decision to announce extra spending for the NHS and to frame it specifically as a benefit of leaving the EU has been widely seen as a sop by May to hardline Brexiters in her cabinet and on the Tory backbenches ahead of some potentially crucial votes this week on the EU withdrawal bill.

Boris Johnson, the foreign secretary, who has stood by the EU referendum bus slogan that departure would free up £350m a week extra for the NHS, tweeted:

Boris Johnson (@BorisJohnson) Fantastic news on NHS funding - a down payment on the cash we will soon get back from our EU payments. #TakeBackControl #BrexitDividend

The gambit is likely to trouble other Conservatives, however, both in terms of whether the increase could instead mean higher taxes or more borrowing, and if it would even deliver a noticeable improvement to NHS services.

In another tweet, Wollaston said the increase, amounting to a 3.4% rise in real terms, would not improve matters without extra money for preventative treatments, social care and capital budgets.

The Local Government Association, which represents councils, said the NHS “cannot thrive” without new social care funding to keep people out of hospital and free up beds.

The IFS has previously said a 5% real-terms increase would be required for real change. The institute’s head, Paul Johnson, noted that 3.4% was higher than recent increases, but still below the long-term average.

Johnson told BBC1’s Sunday Politics that the EU money for the next few years had already been allocated, and that the government’s Office for Budget Responsibility said Brexit would initially erode public finances by about £15bn a year.

Boris Johnson’s £350m claim is devious and bogus. Here’s why | John Lichfield Read more

“It could be a bit more, it could be a bit less,” he said. “As a pure, sort of arithmetic point of view, over this period, there’s no money.”

May was vague on where else the money could come from, telling the Andrew Marr Show that the UK would be “contributing more as a country” and more details would be announced later.

Labour and the Liberal Democrats called for greater clarity on the spending boost. The shadow foreign secretary, Emily Thornberry, said she would “certainly welcome it if we could believe it”.

Thornberry told Marr: “They’ve told us they’re going to pay for it from a Brexit dividend. We don’t really know what that means because we don’t know what the deal is going to be and what the overall effect on the economy is going to be, and actually whether Brexit is going to end up costing us a great deal of money.”

Q&A What are the financial pressures on the NHS that have built up over the last decade? Show Hide Between 2010-11 and 2016-17, health spending increased by an average of 1.2% above inflation and increases are due to continue in real terms at a similar rate until the end of this parliament. This is far below the annual inflation-proof growth rate that the NHS enjoyed before 2010 of almost 4% stretching back to the 1950s. As budgets tighten, NHS organisations have been struggling to live within their means. In the financial year 2015-16, acute trusts recorded a deficit of £2.6bn. This was reduced to £800m last year, though only after a £1.8bn bung from the Department of Health, which shows the deficit remained the same year on year. Read a full Q&A on the NHS winter crisis

The Lib Dem Brexit spokesman, Tom Brake, said he had written to the head of the UK Statistics Authority to adjudicate on whether a Brexit dividend might actually exist.

The issue is likely to pursue May at her speech in London on Monday, where she plans to talk about her personal commitment to the NHS, the work of NHS staff after last year’s Manchester Arena terror attack and her own experiences with type-1 diabetes.

The new money would ensure 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,” May will say, according to extracts released in advance. “This money will be provided specifically for the NHS. And it will be funded in a responsible way.”