Three of the cases were found in England, with the other three located in Scotland.
Authorities are now trying to track down the individual in question and have also contacted other passengers on the same flights of those who have tested positive for the new variant.
The government is urging anyone who took a test on February 12 or 13 and has not received a result, or has an uncompleted test registration card, to contact the NHS on either 119 for England, Wales and Northern Ireland, or 0300 303 2713 for Scotland.
The other two cases in England are from the same household in South Gloucestershire after one person returned from Brazil on 10 February - just days before the government's hotel quarantine rule came into force.
United Kingdom joins France in push to hand vaccines to poorer nations
Canada has been getting all its Pfizer doses from a company facility in Puurs, Belgium, and has experienced disruptions in supply.
Some 5,500 new cases have been reported in the UK.
PHE and NHS Test and Trace are contacting the passengers on Swiss Air flight LX318 travelling from Sao Paulo, through Zurich, and landing in London Heathrow on that date.
He said at the moment, they were very focused on what we're seeing today but warned of the need to start moving away from an "obsession" with each variant as it appears.
"These and other mutations are associated with reduced impact of antibodies against the virus in laboratory experiments", she told Monday's Downing Street press conference."The current vaccines have not yet been studied against this variant and we will need to await further clinical and trial data to understand the vaccine effectiveness against this variant". Only call NHS 111 if you can not cope with your symptoms at home; your condition gets worse; or your symptoms do not get better after seven days. In Scotland anyone with symptoms is advised to self-isolate for seven days.