Theresa May’s claims that the government is putting £10bn extra into the NHS are untrue and the underfunding of the health service is so severe that it may soon trigger rationing of treatment and hospital unit closures, a group of influential MPs have warned Philip Hammond.

Five MPs led by the Conservative Dr Sarah Wollaston, the chair of the Commons health select committee, have written to the chancellor demanding the government abandon its “incorrect” claims of putting £10bn into the NHS annual budget by the end of this parliament and admit the severity of its financial shortage.

“The continued use of the figure of £10bn for the additional health spending up to 2020-21 is not only incorrect but risks giving a false impression that the NHS is awash with cash,” Wollaston and four fellow committee members tell the chancellor in a letter.

“This figure is often combined with a claim that the government ‘has given the NHS what it asked for’. Again, this claim does not stand up to scrutiny as NHS England spending cannot be seen in isolation from other areas of health spending.”

The letter’s other signatures are Dr James Davies, a Conservative MP who is also a family doctor; Labour’s Ben Bradshaw, a former health minister, Labour MP Emma Reynolds; and Dr Philippa Whitford of the Scottish National party, who is an NHS breast cancer specialist.

Their letter’s detailed rejection of the government’s claims raises serious questions about the accuracy of May’s insistence, in a newspaper interview on 17 October and again at prime minister’s questions two days later, that her administration was giving NHS England boss Simon Stevens even more than he had sought in negotiations with ministers.

May told the Manchester Evening News: “Simon Stevens was asked to come forward with a five-year plan for the NHS. He said that it needed £8bn extra; the government has not just given him £8bn extra, we’ve given him £10bn extra. As I say, we have given the NHS more than the extra money they said they wanted for their five-year plan.”