There have been 11 coronavirus cases in Bristol involving "mutations of concern", according to Matt Hancock.
The Health Secretary said people must "continue to act with caution" as he told the Commons where in the country Covid-19 cases with concerning mutations have been confirmed.
Matt Hancock says testing will be increased in the city to people aged 16 and over. He says people should stay at home and should only leave home "where it is absolutely essential".
A Public Health England spokesperson said: “Public Health England has identified 11 cases of the Variant of Concern VOC202012/01, which genomic sequencing has shown to feature the spike protein mutation E484K, predominantly situated within the South West.
“PHE is monitoring the situation closely and all necessary public health interventions are being undertaken, including enhanced contact tracing and control measures.”
The Government is putting in extra testing and sequencing every positive test in areas confirmed to have the Covid variant.
Mr Hancock said: "Working with local authorities we're going door to door to test everyone in those areas and mobile testing units will be deployed offering PCR tests to people who have to leave their home for work or other essential reasons.
"We have also seen 11 cases of mutations of concern in Bristol and 32 in Liverpool, and are taking the same approach."
In a statement, Mr Hancock set out the UK's progress with its vaccination programme and told the Commons: "Despite this optimistic backdrop we must continue to act with caution, not least because of the renewed challenges posed by new variants of the coronavirus.
"We have found here 105 cases of the variant first identified in South Africa including 11 cases which don't appear to have any links to international travel."
He said the aim of the UK in relation to the South Africa variant of Covid-19 must be to "stop its spread altogether".
He said: "As with the variant first identified here in the UK there is currently no evidence to suggest it is any more severe but we have to come down on it hard.
"Our mission must be to stop its spread altogether and break those chains of transmission."