Five Brits, including a child, have been diagnosed with the coronavirus in France.
It comes after they came into contact with a person who had been in Singapore, Health Minister Agnes Buzyn said on Saturday.
The minister said they were not in a serious condition. The total number of people infected with the virus in France has now reached 11.
Ms Buzyn said the group of newly-infected people with the virus formed “a cluster, a grouping around one original case.”
“That original case was brought to our attention last night, it is a British national who had returned from Singapore where he had stayed between January 20 and 23, and he arrived in France on January 24 for four days,” she said.
She added that the latest outbreak had occurred in the mountainous region of Savoie in eastern France.
The death toll in the coronavirus outbreak in mainland China rose to 722 on Saturday, while new cases jumped to 34,546.
The Department of Health and Social Care said that 620 people in the UK have been tested for coronavirus as of 2pm on Friday, with three cases confirmed.
It is understood that the third person in the UK to be diagnosed with coronavirus caught the illness in Singapore.
He is reported to be a middle-aged British man and is understood to be the first UK national to contract the disease.
Around 150 British nationals are to be flown back from the coronavirus-hit city of Wuhan on Sunday and quarantined at a facility in Milton Keynes.
Two earlier flights transporting UK citizens as evacuees from the city – the epicentre of the virus outbreak – are at Arrowe Park Hospital on the Wirral.
Three people have been confirmed to have coronavirus in the UK so far.
South Central Ambulance Service said that Kents Hill Park, a conference centre and hotel, will be used to house the next returning Britons after they land at RAF Brize Norton.
The individuals will remain at the site in isolation for 14 days, it added.
On Tuesday, Foreign Secretary Dominic Raab said that the flight would be the final service chartered by the Foreign Office to bring UK nationals back from the Chinese city.
The ambulance service said the presence of the group in Milton Keynes, Buckinghamshire, does not present a risk to local people.
The first group of Britons who returned on a flight last month are continuing their period of quarantine at Arrowe Park Hospital on the Wirral.