The new health secretary, Sajid Javid, has warned that NHS waiting lists could rocket to 13m in the coming months as concerns rise over the backlog faced by the health service.

Speaking to the Sunday Telegraph, Javid said the growing number of people waiting for non-Covid treatment on the NHS had been what shocked him the most since returning to the cabinet following Matt Hancock’s resignation.

“What shocked me the most is when I was told that the waiting list is going to get a lot worse before it gets better,” he said.

“It’s gone up from 3.5m to 5.3m as of today, and I said to the officials so what do you mean ‘a lot worse’, thinking maybe it goes from 5.3m to 6m, 7m. They said no, it’s going to go up by millions … it could go as high as 13m.

“Hearing that figure of 13m, it has absolutely focused my mind, and it’s going to be one of my top priorities to deal with because we can’t have that.”

It comes as NHS trusts are facing the combined hit of Covid cases rising again, the backlog for other treatments including cancer checks and heart disease, and staff shortages due to workers having to self-isolate if they are “pinged” by the Covid app.

NHS Providers, the membership organisation for NHS trusts in England, warned that up to a fifth of staff could be absent from one trust in just three weeks from now, potentially leading to the cancellation of as many as 900 operations.

Javid confirmed to the Sunday Telegraph that there was “every reason to think that we can take a more proportionate and balanced approach to the isolation policy” for NHS staff after No 10 suggested they could be exempt from having to stay at home if they had two jabs.

He also discussed NHS pay and that raising taxes to fund social care could be a “practical and obvious” solution.

Earlier, Prof Helen Stokes-Lampard, chairwoman of the Academy of Medical Royal Colleges, said deaths were beginning to rise again too. She told BBC Radio 4’s Today programme: “We’ve only just heard in this bulletin about the rising numbers of cases, the rising numbers of people requiring hospital treatment, in intensive care and sadly deaths are starting to rise again, too.

“There seems to be a misapprehension that life will return to normal from then (19 July), and that we can throw away all the precautions, and frankly, that would be dangerous.”

The rate of new cases of coronavirus in most areas of England is now back at levels last seen during the winter. Patient numbers have risen to levels last seen about three months ago.

And there has been a very slight increase in the average number of deaths reported each day of people in England who died within 28 days of testing positive for Covid-19.

But this is still far below the sort of numbers seen in January and February of this year.

The Academy of Medical Royal Colleges said in a statement: “There is little doubt that things will get worse before they get better.”