The UK has recorded the highest number of daily Covid-19 cases since the beginning of the pandemic, with 78,610 reported on Wednesday.
The previous record was 68,053 on 8 January – when the UK was in lockdown.
Speaking alongside Prof Whitty, Prime Minister Boris Johnson said it was “absolutely vital” that everyone gets a booster jab.
“I’m afraid we have to be realistic that records will be broken a lot over the next few weeks as the rates continue to go up,” he added.
Asked whether people should be going to Christmas or New Year parties, Prof Whitty: “Don’t mix with people you don’t have to.
“[You] don’t need a medical degree to realise that is a sensible thing to do with an incredibly infectious virus.”
He encouraged people to take tests before visiting vulnerable people and to meet in areas of good ventilation or outdoors if possible.
The prime minister said the government was not cancelling Christmas events by restricting gatherings or closing pubs and restaurants, but cautioned people to think carefully about the socialising they did.