LONDON — England’s chief medical officer warned Monday that the coming weeks would be the worst of the pandemic for the National Health Service as he appealed to the public to strictly follow guidelines meant to prevent the spread of the disease.

Chris Whitty said political leaders are considering tightening the rules as a new, more transmissible variant of COVID-19 aggravates an already difficult situation. Hospitals are overflowing and exhausted medical staff are under strain.

“I think everybody accepts that this is the most dangerous time we’ve really had in terms of numbers into the NHS,’’ Whitty told the BBC.

English hospitals are now treating 55% more COVID-19 cases than during the first peak of the pandemic in April.

England last week entered a third national lockdown that closed all nonessential shops, schools, colleges and universities for at least six weeks. But police report many violations of rules that require people to stay home except for essential reasons.

Seven new large-scale vaccination centers were opening Monday, joining around 1,000 other sites across the country. The U.K. government’s goal is to vaccinate 15 million people by mid-February.