The three cases of the Manaus strain identified in Scotland correspond to residents who returned from a trip to Brazil and made a stopover in Paris and London.
The Today programme asks whether there is work on a vaccine for the Brazil variant.
Mr Hancock said current coronavirus vaccines being used in the United Kingdom "have not yet been studied against this variant and we're working to understand what impact it might have".
However, experts said that the situation in the United Kingdom was very different to that in Brazil and there was still cause for "optimism", not concern. Scientists say the variant is more transmissible and may be more resistant to existing vaccines than the original virus, and may be able to infect people who have previously had Covid-19.
He said: "We're stepping up our testing and sequencing in south Gloucestershire as a precaution".
There is "no information to suggest the variant has spread further" than that area, Mr Hancock said.
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He said "President Trump has flaws" but that he had made the party more approachable for working-class Americans. CPAC is an event organized by the American Conservative Union, whose chairman, Matt Schlapp, is close to Trump.
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This could see masks only being made mandatory for indoor setting like shopping centres, supermarkets and on public transport. In gyms, the density limit remains one per four square metres, with exercise classes limited to 50 indoors and 100 outdoors.
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AstraZeneca's vaccine was deemed to be about 70 per cent effective in testing. The best vaccine choice, they said, is the one you can get the soonest.
He said the two main variants of concern were the South African and Brazil variant because they were "distributing themselves to many countries". All those aside from the missing case have been told to self-isolate.
The mystery sufferer didn't fill in their test registration card, meaning details of their whereabouts are unavailable.
Boris Johnson has defended the UK's border and quarantine measures, as officials continue to search for a person infected with the new Brazilian variant of the virus before hotel quarantine was introduced.
Had the policy, which was announced weeks before it was implemented, been in force sooner it is likely it would have contained the Brazilian variant, critics have contended.
"Incidents like this are rare and only occur in around 0.1% of tests".
Prof Peacock, also an adviser on the Government's Scientific Advisory Group for Emergencies (Sage), said mutations around the globe were very similar and now appeared to have plateaued.
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