Prof Andrew Hayward suggested tougher measures may be necessary to deal with rising numbers of infections.
Health Secretary Matt Hancock will announce any changes to England's tier restrictions on Wednesday.
Hospitals in England are currently treating more Covid patients than at the peak of the first wave in April.
Mr Hancock said in a tweet that the NHS was facing "unprecedented pressures" from coronavirus, while NHS England's chief executive Simon Stevens said health workers were "back in the eye of the storm".
On Monday, a record 41,385 new Covid cases were reported in the UK, though it is thought the infection rate was higher during spring when testing was much more limited.