Theresa May has refused to say which taxes will rise to pay for her £20bn a year NHS boost, amid a storm of criticism over her claim of a “Brexit dividend” to part fund it.

Pressed on her admission that tax hikes will be needed, the prime minister gave no details, saying only that “we will be contributing more as a country”.

Meanwhile, independent experts and a senior Tory MP dismissed Ms May’s claim – echoing the much-derided Leave campaign – that the government would have extra cash from leaving the EU.

“Don’t even begin to swallow any rubbish that this will be some Brexit bonanza,” tweeted Sarah Wollaston, the Tory chair of the Commons Health Committee.

“In reality the tax rises & borrowing will need to be higher as a result.”

Paul Johnson, the head of the respected Institute for Fiscal Studies (IFS), said the government had accepted that Brexit would swipe £15bn a year from revenues – or £300m a week.

Furthermore, the “divorce bill”, plus commitments to replace Brussels funding in key areas, would swallow up all of the returning EU contributions until 2022.

“There is no Brexit dividend,” Mr Johnson said.

Quizzed by the BBC’s Andrew Marr on the tax rises to come, Ms May said: “The chancellor will announce the details in due course.”

And she claimed: “There are many aspects that will change over the next few months potentially. We will be looking at economic growth and at other issues.”

NHS in Crisis march: in pictures Show all 25 1 /25 NHS in Crisis march: in pictures NHS in Crisis march: in pictures Protesters call on the government to reverse cuts to the NHS. Rex NHS in Crisis march: in pictures Demonstrators dressed as an undertaker and carrying a fake coffin. Getty Images NHS in Crisis march: in pictures Demonstrators gather on Gover Street in central London ahead of a march towards Downing Street to protest against underfunding and privatisation of the NHS and demand an end to the winter crisis in the health service. Rex NHS in Crisis march: in pictures Health workers and NHS campaigners march through London to a rally outside Downing Street. Rex NHS in Crisis march: in pictures Thousands of protesters marched during the demonstration organised by 'The People's Assembly Against Austerity' campaign group that called for better funding for the National Health Service (NHS) to end the 'winter crisis' in the national health care system. EPA NHS in Crisis march: in pictures A Boris Johnson impersonator lies in a makeshift hospital bed next to an effigy of Theresa May during a People's Assembly demonstration against the Conservative government's health policy. Getty NHS in Crisis march: in pictures A demonstrator in a mobility scooter carries a placard. Getty NHS in Crisis march: in pictures Demonstrators take part in a emergency NHS 'Fix It Now' protest demanding an end to the funding crisis in the Health Service. Rex NHS in Crisis march: in pictures Demonstrators take part in pro-NHS march and protest towards Downing Street in Central London. EPA NHS in Crisis march: in pictures A protestor carries a placard featuring Britain's Health and Social Care Secretary Jeremy Hunt. AFP/Getty NHS in Crisis march: in pictures The demonstration is focused on the current crisis in the National Health Service. Getty NHS in Crisis march: in pictures Demonstrators hold placards and set off flares . Getty NHS in Crisis march: in pictures A demonstrator carries a cardboard skeleton wearing an ambulance uniform . Getty NHS in Crisis march: in pictures Demonstrators hold placards during a People's Assembly demonstration against the Conservative government's health policy Getty NHS in Crisis march: in pictures The Government will be urged to provide more beds, staff and funds to ease the problems facing the service. PA NHS in Crisis march: in pictures Protestors gather calling for an end to the "crisis" in the NHS. AFP/Getty NHS in Crisis march: in pictures Shadow Health Secretary Jon Ashworth M joins people taking part in the march. PA NHS in Crisis march: in pictures A placard reading 'Nurses with fight for the NHS'. AFP/Getty NHS in Crisis march: in pictures Protestors carry placards and shout slogans. AFP/Getty NHS in Crisis march: in pictures People march through central London. PA NHS in Crisis march: in pictures People take part in a march in London in support of the National Health Service. PA NHS in Crisis march: in pictures People hold up a sign in support of the National Health Service to demand an end to the "crisis" in the NHS. PA NHS in Crisis march: in pictures Protestors carry placards featuring Britain's Prime Minister Theresa May and Britain's Health and Social Care Secretary Jeremy Hunt. AFP/Getty NHS in Crisis march: in pictures People take part in a march in London in support of the National Health Service. PA NHS in Crisis march: in pictures Demonstrators carry placards . Getty

Chancellor Philip Hammond is expected to opt for “stealth taxes”, by delaying or scrapping promises to raise income tax thresholds – which will anger many Tory MPs.

But Mr Johnson said that would not come close to bringing in the funds needed, warning it would require “more than a couple of pence” on income tax and adding: “£20bn is a big number.”

The extra £20bn a year, promised by 2023-24, marks a dramatic break with eight years of austerity and follows a difficult battle with the Treasury for more funds.

However, the annual real-terms increase will be around 3.4 per cent, not the 4 per cent pleaded for by Simon Stevens, the outspoken NHS England chief executive.

During the interview, the prime minister also:

* Appeared to admit the £20bn could still be allocated even if Britain stayed in the EU – describing the question as ‘completely hypothetical”

* Hinted the increase in the early years may be less than 3.4 per cent – saying “it may vary a little from year to year”

* Refused to say when cancer waiting targets will finally be hit – they have been missed for more than two years

Labour said it would match the new Tory spending plans and “go further” with extra increases from scrapping corporation tax cuts.

John McDonnell, the shadow chancellor, described them as “a pre-election gimmick”, saying: “Can you imagine if I came forward with this?

“There would be accusations of magic money trees – it’s a magic money forest that has come out this morning.”