Boris Johnson has said he is "optimistic" that people will be able to take summer holidays this year but warned it is too early to lift restrictions.
Speaking during a visit to west Yorkshire on Monday the prime minister said there were signs lockdown measures were working but it was too early to "take your foot off the throat of the beast".
"We are starting to see some signs of a flattening and maybe even a falling off of infection rates and hospitalisations," he told reporters.
"But don't forget that they are still at a very high level by comparison with most points in the last 12 months, a really very high level.
"So the risk is if you take your foot off the throat of the beast … and you allow things to get out of control again then you could, alas, see the disease spreading again fast before we have got enough vaccines into people's arms. That's the risk."
Mr Johnson added that he could not give "concrete" dates for the lifting of restrictions, though said he was "optimistic" about the possibility of summer holidays.
But he added that "some things have got to go right".
"The vaccine programme has got to continue to be successful," he said.
"We have got to make sure we don't get thrown off course by new variants, we have got to make sure that we continue to keep the disease under control and the level of infections come down."
Mr Johnson was speaking as the government announced that urgent community testing for a new South African variant of Covid-19 would take place in eight areas across the country.
People aged over 16s in eight areas in Surrey, London, Kent, Hertfordshire and Walsall will be asked to take tests, with mobile tracking units sent to out to neighbourhoods.
Like the UK variant, the South African variant is though to be more contagious than the original strain of Covid-19.
There is some evidence that the strain might make vaccines slightly less effective, however.
But Mr Johnson told reporters: "It's very, very important that our vaccines continue to develop and to adapt – and they will."
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