The government may have to spend up to £40 billion to try to repair NHS waiting times and end the long delays being faced by patients, according to unpublished Downing Street estimates.

The figures, disclosed by Whitehall sources, underline the huge scale of the challenge in getting NHS waiting times back to manageable levels before the next election. The calculations highlight how the Prime Minister may have to commit anywhere between £2 billion and £10 billion a year for up to four years, on top of core NHS funding, to tackle hospital waiting lists.

The total number of people waiting for hospital treatment, especially surgery, had topped five million for the first time. The figure stood at 5,122,017 in April, the highest since records began in 2007. NHS England plans to give Downing Street a detailed analysis soon of how long it will take to start providing care again within its existing set of targets, to help inform No 10’s thinking before the comprehensive spending review in the autumn.

The leaked projections were put together by the Cabinet Office as part of its work looking at the scale of post-coronavirus support needed in health, education and justice.

Of the 5.1 million, almost 400,000 people have had to wait more than a year for treatment for conditions including cancer and heart problems, hip and knee replacements and cataract removals. A small number – 2,722 – have already been waiting longer than two years.