There is "no risk-free way of travelling overseas", Downing Street has warned after Boris Johnson said he would "not hesitate" to impose quarantine for other countries.
The Government is expected to strike France from the "green list" of quarantine-free countries later this week after the Joint Biosecurity Centre (JBC) meets on Tuesday to analyse the latest data on coronavirus cases across the world.
Other countries at risk of being dropped include the Netherlands, Switzerland, Poland and Malta, while there are hopes that Portugal may be reinstated.
Number 10 said it would not hesitate to "act rapidly" to remove countries from quarantine-free travel in response to rising cases.
The Prime Minister's official spokesman said: "We have been updating the exemptions list on a weekly basis in order to make sure that it reflects the changes in the international health picture.
"Unfortunately, during this pandemic there isn't a risk-free way of travelling overseas. The population's made a huge effort to get the disease down to the levels that we're seeing in the UK, and if we feel that we need to act in relation to the travel exemptions list, then we'll do so."
On a visit to a school in east London on Sunday, Mr Johnson said that while he did not want to "advise people" about their holiday decisions, he urged Britons to check Foreign Office advice before travelling.
He said: "In the context of a global pandemic, we've got to keep looking at the data in all the countries to which British people want to travel. Where it is necessary to impose restrictions or to impose a quarantine system, we will not hesitate to do so.
"It's been a huge effort for the entire population of this country to get the disease down to the levels that we are currently seeing, but we do not want reinfection and that's why we've got to keep a very, very close eye on the data in destinations around the world."
The JBC will meet on Tuesday to analyse the latest global data on coronavirus before the Government makes an updated quarantine announcement on Thursday.
The level of risk will be calculated based on individual countries' incidence rates, trends in the number of cases and estimates of the proportion of the population with coronavirus.
Each nation's testing capacity, transmission status and the quality of data available will also be assessed.
A Government source said that France's data was at a "concern level" when it was analysed last week.
Travel industry figures warned that the French "won't lie down" and accept new quarantine rules without retaliation.
Noel Josephides, the director of the Association of Independent Tour Operators, said: "If the Government does take this course of action, France will turn around and say: 'We're testing more, why don't you test more people?'
"If they pick on France, they won't lie down like Spain or Portugal. There is already diplomatic tension over the Channel issues. I would be surprised if France didn't make any reciprocal moves."
He added that speculation had left both the industry and customers "completely confused" and risked harming the already beleaguered travel industry further.
Mr Josephides added: "The Government is doing its best to frighten people from travelling abroad. It's hint after hint, it's rumour after rumour, and all it does is destroy people's confidence. It confuses them and they choose not to travel. That's a recipe of disaster for the travel industry."
Meanwhile, Paul Charles, the founder of travel consultancy the PC Agency, said France has just a matter of hours to get its case numbers down in order to avoid being struck off the "green list".
Writing for The Telegraph, he said the chance of this happening is "highly unlikely, despite face masks now being mandatory in many outdoor public spaces, not just indoors in shops".
Sir Iain Duncan Smith, the former Conservative leader, said that to issue a blanket quarantine on any new country would be "madness" and instead urged the Government to "quickly adopt a targeted regional approach".
He said: "There are lots of people that have gone on holiday to France, and they risk potentially being stuck if the Government changes its advice. France is a big country with differing infection rates in different regions.
"It's madness, it needs better planning. What we're getting at the moment is a bunch of scientists trying to scare everyone to death. We are lurching around all over the place and it's very bad news for the travel industry."