Boris Johnson warned coronavirus cases could rise again after schools reopened on Monday.
The prime minister also appeared to reject suggestions that his “roadmap” to lifting lockdown in England could be accelerated as Covid cases, deaths and hospitalisations all continue to fall.
Johnson pointed towards Europe, where Covid cases have risen by around 9% in recent weeks, and warned that the UK has experienced similar increases after the continent in the past.
It came as England’s deputy chief medical officer Jenny Harries said infections were now below 100 per every 100,000 people – levels last seen in September.
Asked whether the encouraging data suggested lockdown could be lifted more quickly, the PM told a Downing Street briefing: “Of course I understand the urgency that people feel but we have to be driven by the data, we have to look at the rates of infection.
“Don’t forget they are still very high by the standards of last year – we still have thousands of people in hospital with Covid.
“We have seen, alas, in other European countries that the curve is going up again and we remember frankly what happened every time we’ve seen those upwards curves in our friends and neighbours that it is not too long after that that we see an increase in this country as well.
“We’ve just got to remain prudent and the whole point about this road map is it is intended to be cautious but irreversible and we think we can do that because of the success of the vaccine rollout.
“I think people would really rather trade some urgency and some haste in favour of security and certainty about those dates that we have set out.”
Harries meanwhile warned that despite cases plummeting, they were at “a level at which a new wave could easily take off from again”.
The deputy chief medical officer did however downplay suggestions schools may be forced to close again if new cases emerge.
She told the briefing: “I think we can be very optimistic going forward.
“The testing programme in schools should mean that the likelihood of a case going into a school and then numbers of children having to come out of education to isolate should be very significantly reduced.
“There may be a very short period at the start of this programme where everybody gets used to it and a larger number of children come out of school and then it will settle down.
“It is really important when observing this that people think through the next three to four weeks, not the first one or two.”