The chief scientific officer, speaking at a Downing Street press conference on Monday, said the virus is resurgent and “measures need to be increased” in the coming days “not reduced”.
Scientists estimate the new variant, which first emerged in Kent, is up to 70% more infectious.
“Evidence of this virus is it spreads easily, it’s more transmissible,” Vallance said.
“We absolutely need to make sure we have the right level of restrictions in place.
“I think it is likely that this will grow in numbers of the variant across the country and I think it’s likely therefore that measures need to be increased in some places in due course, not reduced.
“It is the case that this will spread more.”
Last week, the government effectively cancelled Christmas for millions of people with strict new curbs covering London and huge swathes of the south-east in tier 4.
In other tiers areas, which include much of the north, up to three households can mix on Christmas Day, however.
Boris Johnson chaired an emergency Cobra meeting on Monday amid travel chaos at Dover after France imposed a travel ban on UK freight.
The prime minister said he and French president Emmanuel Macron had spoken about the block and were committed to resolving it, amid fears the UK could face food shortages.
Johnson aimed to strike an upbeat tone and revealed that 500,000 people had been vaccinated against Covid so far.
But amid calls from scientists for the government to consider closing schools again, Johnson appeared to water down the government’s commitment, saying ministers would keep schools open “if we possibly can”.
Adding the UK “can certainly look forward to a very, very different world” from Easter, he said: “It’s very, very important, not just for people’s morale, but it’s also totally realistic.
“We have every reason to be extremely hopeful about this country’s ability to bounce back next year from Covid, and I think that is the right thing to say then and now.”
Vallance also attempted to reassure the public by saying there was no evidence the new strain was more fatal.
He said: “Evidence that this can transmit more readily is becoming clear in terms of the data of the rapid spread of this virus across areas.
“The transmission is increased, but we can’t say exactly by how much, but it is clearly substantially increased, so it is more transmissible, which is why we see it growing so fast and spreading to so many areas.
“There is no evidence that the disease course is any different, so if you catch it the disease looks the same as any other form of Covid infection.
“In terms of the immune response, there is nothing to suggest that this won’t have the same susceptibility to antibody attack from vaccine or pre-existing infection as any other form.
“At the moment, the vaccine looks as though it should be as effective and that’s obviously being looked at.”