Coronavirus testers will go door-to-door in areas of England as part of an urgent effort to swab 80,000 people in an attempt to halt the spread of the South African strain.
Eleven cases of the variant have been identified over the last five or six days in people who have no links to travel – suggesting it may be spreading in communities.
Matt Hancock told a Downing Street press conference the "stay at home" message was particularly important in areas where the South African variant had been identified amid concerns that vaccines may have diminished effectiveness against the mutation.
Experts from Public Health England (PHE), who have been sequencing around 5% to 10% of all positive cases looking for variants, are now hoping to break any chains of transmission. All but two areas involved single cases of the variant.
Mobile testing units and some home testing kits are being sent into eight postcode areas: Hanwell, west London; Tottenham, north London; Mitcham, south London; Walsall in the West Midlands; Broxbourne, Hertfordshire; Maidstone, Kent; Woking, Surrey; and Southport, Merseyside.
The South African variant is thought to be as transmissible as the variant that was first identified in Kent but there is no evidence yet that it causes more severe disease.
Health Secretary Mr Hancock said the UK has now identified 105 cases of the South Africa variant, 11 of which have no links to international travel.
As the door-to-door testing and enhanced contact tracing effort was launched, Mr Hancock said "we need to come down on it hard".
"We are sending in the extra surge testing and the enhanced contact tracing to try to stop those chains of transmission, to stop the spread altogether of these new variants, but it is not straightforward," he said.
"There may be further cases that we don't know about yet and our genomic sequencing is in place to try to spot them."
It was "absolutely vital" that people minimise all social contact in the areas where South African cases had been identified, he said.
Public Health England's Dr Susan Hopkins said three different vaccines trialled so far had shown effectiveness against the South African variant at a level higher than the minimum standard set by the World Health Organisation and the US Food and Drug Administration.
"We expect all other vaccines to have a similar level of effectiveness, particularly in reducing hospitalisation and death," she said, adding that laboratory studies were being carried out to provide further evidence.
She said the UK was looking at whether those who had already taken a Covid-19 vaccine would need a booster shot to cover the risk posed by new mutations "a bit like the annual flu vaccine".
The South African variant had more mutations than the UK strain in the coronavirus spike protein which meant vaccines could have "diminished" effectiveness but were still "very good".
Dr Hopkins said it was essential to break the chains of transmission to prevent the virus developing further mutations.
Concerns about the South African variant came as there were more positive developments in the vaccine rollout.
Mr Hancock said almost nine in 10 of all those aged over 80 had been vaccinated, with over half of those in their 70s receiving a jab.
He added: "We have visited every single care home with older residents in England and offered vaccinations to all of their residents and staff – this has been an incredible example of health and social care working together."
Government data up to January 31 shows 9,296,367 first doses have been given, a rise of 319,038 in 24 hours.
Based on the latest figures, an average of 407,402 first doses of vaccine would be needed each day in order to meet the Government's target of 15 million first doses by February 15.
Official figures showed a further 406 people had died within 28 days of testing positive for Covid-19 as of Monday, bringing the UK total to 106,564.
There had been a further 18,607 lab-confirmed cases of coronavirus in the UK – the lowest daily total of new cases since December 15.
Prime Minister Boris Johnson said while there were signs the lockdown measures were working it was too early to "take your foot off the throat of the beast" by easing restrictions.
And he suggested that England might not return to a regional system of coronavirus controls as he was keeping an "open mind" about a blanket approach across the country when the time comes to ease the lockdown.
In other developments:
– Nicola Sturgeon defended the speed of the coronavirus vaccine rollout in Scotland but said she did not know why vaccination figures were "dipping a little bit on a Sunday" after just 9,628 patients received their first vaccine dose.
– The Government has ordered an extra 40 million doses of the Valneva Covid-19 vaccine, which has not yet been approved for use.
– The UK could be easing out of restrictions in March and back to almost normal by summer if vaccines are 70% to 80% effective at blocking transmission, Dr Mike Tildesley, a member of Scientific Pandemic Influenza Group on Modelling (Spi-M) said.