The prime minister’s announcement comes amid mounting pressure from within Conservative ranks, led by Jeremy Hunt and Boris Johnson, for her to ditch the small spending rises the NHS has received since 2010 and start giving it increases stretching to many billions of pounds a year.

May did not mention how much more money the long-term plan could involve. But the Office of Budget Responsibility has calculated that getting back to the rises that the NHS received from its creation in 1948 until 2010, an average of almost 4%, would need the NHS budget to jump to about £150bn by 2022-23.

That is £20bn more than currently planned and a huge increase on the £125bn that has gone into health in England this year.

Speaking to Commons select committee chairs today, the prime minister promised to outline the details of the plan before Easter 2018 and said it would precede the spending review already planned in summer 2019.

Responding to questions from the Tory MP Sarah Wollaston, the chair of the health and social care select committee, May said: “This year and in advance of next year’s spending review I do want to come forward with a long-term plan. I want that to be done in conjunction with NHS leaders and provide a multiyear funding settlement consistent with our fiscal rules and balanced approach.

“Ensuring the NHS can cope with demand ahead of the spending review, I would suggest we can’t wait until next Easter. I think in this 70th anniversary year of the NHS’s foundation we need an answer on this.”

May’s move comes after days of speculation that she and the chancellor, Philip Hammond, are looking into a new tax as a potential way of raising extra money to plough into the NHS. They are considering giving the NHS a £4bn “birthday present” to mark its 70th birthday on 5 July, according to reports.

Simon Stevens, the chief executive of NHS England, whose lobbying for higher government funding for the increasingly beleaguered service has previously irritated May, said her promise was “very welcome, timely and significant”.

“The NHS celebrates seven decades of service this July at a time of great pressure on frontline staff and great promise for improved care. Charting a multiyear path for modern, efficient and sensibly funded health and social care could mean huge gains for cancer patients, mental health services and support for frail older people, as well as the several million nurses, doctors and other care staff who devote their lives to looking after us,” he added.

May added that “I do share a lot of the diagnosis” of the NHS’s problems contained in a letter sent to her on Monday by 21 MPs, which warned that Britain’s health and social care systems are too underfunded to discharge their duties properly.

Taxes will have to rise to give the NHS the money it needs, said Prof Anita Charlesworth, the director of economics and research at the Health Foundation.

“A commitment to long-term stable funding for the NHS is a really important development. A 10-year settlement will span a general election and, if it is to hold, there will need to be cross-party support.

“All independent analysis suggests that the NHS and care system need increases of about 4% a year above inflation. Funding increases at that level can’t be found from within the government’s current spending envelope and would be a big increase in borrowing so must mean that taxes are going to have to rise.”

Jonathan Ashworth, Labour’s health and social care spokesman said: “Years of starving the NHS of the funds it needs resulted in the worst winter crisis on record, the ongoing drastic shortage of healthcare staff and the abandoning of minimum legal standards of care which patients are entitled to.

“Labour has repeatedly called for a long-term investment plan for the NHS. Unlike the Tories, Labour would fund the NHS by an extra £5bn this year, end privatisation and secure the sustainable future of social care.”

Meanwhile, in another announcement intended to show that ministers are making serious efforts to improve the ailing NHS, Hunt has pledged a £760m tranche of new capital funding to finance the building of health facilities such as urgent care centres, and new diagnostic and mental health services.

The money will help support transformation of the way NHS staff care for patients as part of NHS England’s Five-Year Forward View plan to deliver more care outside of hospitals to help prevent avoidable, expensive stays in hospital through partnerships that have been created across England.

The £760m is part of £2.9bn that ministers have pledged to spend between 2017 and 2023 to improve existing, and build new, NHS facilities. It follows several years of Hunt’s Department of Health and Social Care raiding the NHS’s capital budget – by as much as £1.2bn a year – in order to give hospitals more money to try to cope with an ongoing rise in demand for care.