Theresa May is being urged to write off almost £12bn in overspending by hospitals or risk her £20bn NHS boost being spent on debt repayment rather than improving healthcare.

NHS experts are warning that promised expansions of cancer and mental healthcare will prove impossible because a large amount of the £20bn that the prime minister pledged this year will go to the NHS by 2023-24 will be used servicing historic debts.

The calls to wipe out £11.7bn of deficits and loans are being led by Peter Carter, who NHS bosses hired to help turn around two hospital trusts in Kent in 2016 and 2017, and come a week before the budget, in which Philip Hammond will explain how the government will find the £20bn it announced in June to mark the NHS’s 70th anniversary.

The debts “are a millstone which has to be removed from around the neck of the NHS”, said Carter, an ex-chief executive of the Royal College of Nursing. “Having to service the debt will significantly compromise the impact of the 3.4% [annual NHS budget rises May has pledged until 2023] to such an extent that new money will not enable the NHS to modernise; it will in effect help the NHS to stand still.”

“The impact of writing off the debt will have minimal effect on the national debt but will have a major impact on the ability of the NHS to maximise the new investment the government is promising”, added Carter. The NHS in England overspent by £4.3bn last year, while the 240 NHS trusts owe the Department of Health and Social Care £7.4bn in outstanding historic loans. NHS finance experts from the King’s Fund and Nuffield Trust thinktanks blamed the debt pile on persistent NHS underfunding of the NHS.

Saffron Cordery, the deputy chief executive of NHS Providers, which represents trusts, said hospitals backed Carter’s call. He said hospitals needed to be helped to get back to doing their jobs without ending up in deficit, as two-thirds did last year.