The Government has refused to deny that tourists returning from Croatia and Greece could face quarantine measures.
This comes after an increase in the number of coronavirus cases in both countries over the past week.
A No 10 spokesman said the Government "continue to keep these rules under review" and that "protecting public health" remains the main priority.
Defending the short notice of the Government's policy change in adding France to the quarantine list on Saturday morning, the spokesman added: "It is right that we take quick action to prevent cases being imported into the UK."
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It came as the number of cases per 100,000 people in Croatia has reportedly risen above 20, seen as a key benchmark.
Meanwhile, cases in fellow popular summer holiday destination Greece have also increased during August.
The No 10 spokesman said: "We continue to keep these rules under constant review and we publish a list of the countries and territories that we are concerned about. You'll have seen the last update as of last week."
Asked whether Greece and its islands would count as one country for quarantine rule purposes, he added: "As I say, we will continue to keep data for all countries and territories under constant review. We update the list on a weekly basis."
Pushed on the limited time between new quarantine measures being announced and their implementation, the No 10 spokesman said: "We've always said that protecting public health remains our top priority, which is why it is important that, when we make changes to the exemptions list, we do so in a swift way.
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"While these changes we understand can be disruptive, it is right that we take quick action to prevent cases being imported into the UK."
Travellers from countries on the quarantine list are asked to provide an address where they will self-isolate for 14 days after their arrival in England.
People who do not self-isolate can be fined up to £1,000 in England, Wales and Northern Ireland, with fines of £5,000 for persistent offenders.
Scotland, Wales and Northern Ireland can make their own quarantine rules.
Asked if people returning from countries which are not exempt from the 14-day quarantine are able to do a big supermarket shop on their way home before isolating, the No 10 spokesman said: "The guidance is published and clearly sets out what you can and can't do when you are quarantining.
"It specifically says you should not go shopping. If you require help to buy groceries, other shopping or picking up medication, you should ask friends or relatives or a delivery."
