Boris Johnson, the Prime Minister, who will be holidaying in Scotland next week, has encouraged others to take their breaks in the UK.
As well as France, the additional countries from which travellers must now self-isolate for 14 days due to rising cases are the Netherlands, Monaco, Malta, Turks and Caicos and Aruba.
The Sage minutes show experts believed double-testing would pick up more cases, help spot problem routes and ensure people were quarantining.
On arrival, all travellers are required to complete a health declaration form, and it is up to the Border Force and the regional public health authority to ensure that people adhere to the rules.
Priti Patel, the Home Secretary, previously said there had been a high level of compliance. The most recent Home Office figures reveal that just nine fines were issued at the border since quarantine restrictions were introduced and the most recent police figures indicate that only one person was fined.
Lucy Moreton, of the ISU, the union representing Border Force officials, said: “For lots of people who are on holiday and are only just learning that they will have to go into quarantine, this is going to be very difficult. They will just not be prepared to go straight into quarantine for 14 days.”
Government sources said people would be required to organise food shops while on holiday because they would be expected to go into quarantine as soon as they arrived back in Britain.
Linda Bauld, a professor of public health at the University of Edinburgh, said: “Quarantine is a blunt instrument, and the problem is that people break it.
“There are alternatives. The key one is testing travellers on arrival. A more effective system, in my view, would involve a second test some days later, which would reduce the quarantine period from two weeks to one week.”