Jeremy Hunt has refused to spell out how the government’s promised £20bn NHS boost will be paid for, amid a wave of criticism at claims the money could come from the “Brexit dividend”.

The health secretary admitted the move would “increase the burden of taxation”, but he would not confirm whether it would be funded by stealth taxes such as delaying rises in income tax thresholds.

Ahead of the 70th anniversary of the NHS, the prime minister has committed to spending an additional £384m a week – in an echo of the Leave campaign’s widely discredited pledge to return £350m to the health service after Britain leaves the European Union.

However, she faced pressure from MPs and economists over her claim that the cash Britain would have contributed to the EU could fund the 3.4 per cent increase in spending on the health service.

The head of the Institute for Fiscal Studies (IFS) rubbished the idea of a Brexit dividend, while shadow chancellor John McDonnell said claims the funding could come from money sent to Brussels were “just not credible”.

The Office for Budget Responsibility (OBR), which provides independent forecasts for the Treasury, has previously said Brexit could create a £15bn hit to the public finances by the 2020s.

Mr Hunt said that there had been “huge, very difficult” discussions with the Treasury that “went to the wire” over the plans, but insisted that Philip Hammond’s department had “done its sums” to make sure the cash boost was affordable.

“We are clear that there will be an increased burden of taxation,” he told BBC Radio 4’s Today programme.

The health secretary said: “We will be able to explain exactly where every penny is coming from but we will do that in the budget.

“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’.”

He confirmed that the extra cash would not be used to cover social care, but he did not give any extra detail on the long-awaited shake-up of support for elderly and vulnerable people.

Ms May announced the plans in a speech on Monday, and paid tribute to NHS staff who saved the lives of the victims of the Manchester bombing.

She said: “There, in the face of the very worst that humanity can do, I witnessed firsthand the very best.

“Doctors and nurses working 24 hour shifts to treat the injured. Surgeons who were off shift, dropping everything to come in and perform life-saving operations.

“Paramedics who had risked their own lives to get others to safety. In every instance, I was struck not only by the medical expertise of the staff but the compassion with which people were treated.”

Ms May also spoke of her own struggles after being diagnosed with type 1 diabetes, saying: “I would not be doing the job I am doing today without that support.”

Of the increased investment, the prime minister said: “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.

“This must be a plan that ensures every penny is well spent. It must be a plan that tackles waste, reduces bureaucracy and eliminates unacceptable variation, with all these efficiency savings reinvested back into patient care.”​

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

IFS director Paul Johnson said the Brexit windfall would not materialise when the UK stopped paying more than £

He told the BBC’s Sunday Politics: “There isn’t a Brexit dividend. So there isn’t a dividend in two senses.

“First, over this period if you look at the arrangement we have come to with the EU in terms of paying our exit bill, and you add to that the commitments the government has made in terms of funding farmers and so on, there is literally arithmetically no money.

“In addition, we know because the government has accepted this that the public finances will be worse as a result of the Brexit vote.

“The OBR has said by £15bn a year – it could be a bit more, it could be a bit less – because of the economy.”

Tory health committee chair Sarah Wollaston also said claims of a Brexit bonanza were “tosh”.

And John McDonnell told the Today programme: “We need to have confidence in what’s being said. It’s all well and good making an announcement like this and trying to hit the headlines, but to be credible you have to say where the money’s coming from. We certainly haven’t seen that.