Cases have soared in London, with some 36,000 confirmed new infections in the week to December 12.
He repeated his message that the current Christmas rules — which allow three households to mix indoors between 23 and 27 December — were “very much a maximum” and “not a target people should aim for”.
Speaking to reporters on Friday afternoon, Sir Keir said: “[Mr Johnson] has got to toughen up over Christmas, he’s got to show some leadership.
“Easing the restrictions I think is going to be the next big mistake for the Prime Minister.”
“Pressed on what exactly he wants in terms of restrictions over the festive period, Sir Keir said: “In Wales, for example, they brought it down to two households, that seems a step in the right direction, might want to even talk about the numbers within the households.
“But what you can’t have is a Prime Minister who, as he’s done throughout this pandemic, he’s been too slow to act.”
Northern Ireland is set to enter a tough new six-week lockdown on Boxing Day, while Wales will go into its own lockdown two days later.
The Scottish government has said “nothing can be ruled out” ahead of a review on Tuesday.
Professor John Edmunds, who sits on the Scientific Advisory Committee for Emergencies (SAGE), warned on Friday that “very stringent” measures may have to be imposed for a long time to bring the epidemic down to a “safe” level.
“At the moment, it doesn’t look like the tier system is holding the epidemic wave back unfortunately,” he told Sky News.
“So, I think we are going to have to look at these measures and perhaps tighten them up, we really will, that’s a horrible thing to have to say, but we are in quite a difficult position at the moment.”
