The NHS risks ending up with billions of pounds less than anticipated from the government’s flagship funding pledge unless it can secure a further cash injection from the Treasury, it has emerged.

Theresa May announced in the summer that funds for NHS England would be boosted by £20.5bn by 2023-24, in an intervention designed to calm concerns about the pressures on the service and to improve cancer and mental health services. But there are now concerns that an increase in inflation since the pledge was made will see a “substantial” shortfall.

This has added to the problems for Philip Hammond, the chancellor, as he juggles demands for extra funding across Whitehall amid economic uncertainty over Brexit. He now faces a choice between cutting the pledged NHS funding or irritating Conservative MPs by finding even more money for the service.

Many Tories are frustrated that the huge sums committed to the NHS will prevent the party from taking action in areas such as schools and policing.

Hammond has guaranteed that the NHS will be handed a further £20.5bn by 2023-24 in real terms, meaning its funding in that year will be adjusted to take inflation into account. However, uncertainty has emerged over whether the Treasury will fully protect the budget increases for each of the intervening years.

Research by the independent Health Foundation thinktank suggests that in order to deliver the promised percentage increases, the Treasury will have to find £260m more next year, £624m in 2020-21, £897m in 2021-22 and almost £1.1bn in 2022-23. Senior MPs have been alerted to the issue, which is monitored by the health select committee.

The NHS is to reveal its long-term spending plan next month. The Treasury has said it will commit to funding “consistent with that plan”. However, a final settlement will only be approved ahead of the government’s review of all departmental spending, to be unveiled next year.

Anita Charlesworth, director of research and economics at the Health Foundation , said: “The government committed to increase NHS funding in real terms every year for the next five years. Higher inflation will erode that commitment unless it makes good that shortfall in each and every year. It has committed to do this but the issue needs to be settled quickly as there are substantial sums at stake.

The call for more NHS cash adds to the chancellor’s headaches. Photograph: Henry Nicholls/Reuters

“Higher inflation means that without the extra cash the NHS funding increase for next year would be worth £260m less than anticipated for the frontline, and in 2022-23 the gap would rise to around £1bn.

“Sums of this magnitude would have an impact on the pace and scale of improvements in the NHS. Like decisions on funding for capital, workforce training and public health they cannot wait for the outcome of the spending review.”

In the run-up to May’s funding pledge, tensions rose between Simon Stevens, the head of NHS England, and the government.

Stevens had been pressing for annual budget increases of 4% but the final settlement offered annual rises of 3.4%.

At a recent appearance before the Commons public accounts committee, Stevens warned that the original cash settlement offered in the summer “would be lower in real terms than that which the PM set out” unless the Treasury fully adjusted it to take inflation into account.

The Treasury said: “The NHS is our number one spending priority and we have fully funded the cash settlement announced in June. The NHS will come forward with its new long-term plan by the end of the year, and the government will confirm the final settlement consistent with that plan, and the £20.5bn real-terms increase by 2023-24, in the spending review.”