In a briefing in London, Mr Johnson said “storm clouds” were forming elsewhere in Europe because of a rise in deaths and infections and that he could not rule out restrictions over Christmas in England if cases continued to rise in the country.
Almost 40,000 new Covid-19 infections were reported on Monday, compared with 32,208 on the same day last week.
The UK Government said people aged over 40 would be invited to receive booster jabs in the coming weeks.
Thirteen million have already had their third shots.
“It would be an utter tragedy if, after everything we have been through, people who had done the right thing by getting double vaccinated ended up becoming seriously ill or even losing their lives because they allowed their immunity to wane,” Mr Johnson said.
“We don’t yet know the extent to which this new wave will sweep up on our shores, but history shows that we cannot afford to be complacent.
“Those countries with lower vaccination rates have tended to see bigger surges in infection and, in turn, been forced to respond with harsher measures, while those countries with higher vaccination rates have so far fared better.
“It shows us that if we want to control the epidemic here in the UK and if we want to avoid restrictions on our daily lives, we must all get vaccinated as soon as we are eligible.”
England’s chief medical officer, Prof Chris Whitty, said Covid-19 cases and hospital admissions had been “broadly flat” for weeks.
But he said large parts of the National Health Service were under “very significant pressure” and were likely to remain so over the winter.
“But in terms of the Covid numbers, they’re not currently going up in the kind of numbers you’re seeing in continental Europe, but obviously if they did, that would be a situation where we would have to look again at what the situation is at that stage,” Mr Whitty said.
“I think we have got a difficult winter ahead of us. I think that is a widely accepted situation.
“The NHS is a remarkably resilient organisation. But, nevertheless, everybody would accept that large parts of it – particularly the ambulance system but there are others, A&E [hospital emergency department] and others – are under significant pressure and I’m afraid are likely to remain so over the winter period, which is why all health staff would reiterate the point the PM has made about encouraging people to get vaccinated.”
Asked whether he could guarantee there would not be a lockdown over Christmas, Mr Johnson said: “Clearly, we cannot rule anything out and the most important thing people can do to prevent further NPIs from being taken is to – non-pharmaceutical interventions, that is, further restrictions – get the boosters.”
A total of 50,582,504 first doses of Covid-19 vaccine were administered in the UK by November 14, government figures show, 22,938 of which were given in the past 24 hours.
In total, 46,027,909 second doses have been given, an increase of 17,048.
A combined total of 12,860,751 booster and third doses was given, a day-on-day rise of 217,349.
Separate totals for booster and third doses are not available.