Dame Jenny Harries’s warning came after figures showed infections had jumped by more than half a million in just one week.
The UK Health Security Agency chief executive said: “It doesn’t look as though that (current) wave has finished yet, so we would anticipate that hospital cases will rise.”
She added that people should “go about their normal lives but in that precautionary way”, highlighting handwashing, keeping distance where possible and wearing masks in enclosed places.
Speaking about masks, she said: “If I’ve got any respiratory infection it’s a good thing to do.”
Asked if it matters that a lot of people are getting infected with Covid, she said: “Whilst we have an armament now of vaccines and antiviral treatments, we do have… a rise in hospital admissions and occupancy.
“And that means it’s not just Covid that we’re concerned about, but it’s actually our ability to treat other illnesses as well.”
A total of 2.3 million people in private households are estimated to have had the virus last week, up 32 per cent from a week earlier, according to the Office for National Statistics.
This is the highest estimate for total infections since late April, but is still some way below the record of 4.9 million at the peak of the Omicron wave at the end of March.
Dame Jenny appealed to the “nearly 20 per cent of the 75-plus year-old group” who have not had a spring booster to come forward.
Saffron Cordery, the interim chief executive of NHS Providers, said: “Trust leaders know they are in for a bumpy ride over the coming months as they tackle new and unpredictable variants of Covid-19 alongside grappling with seasonal flu pressures which may hit us earlier than usual this year.”