Germany, France, the Netherlands, Denmark and Italy were among those to suspend flights from the UK, while outbound train services through the Channel Tunnel have also been halted.
The Republic of Ireland announced flights arriving from Britain would be banned for 48 hours and non-freight ferry crossings would stop.
Outside of Europe, Canada has also suspended entry of all passenger flights from the UK, with a ban of 72 hours coming into force at 05:00 GMT.
Passengers who arrived in Canada from the UK on Sunday (20 December) would be "subject to secondary screening and enhanced measures, including increased scrutiny of quarantine plans", authorities said.
Other countries and territories to announce restrictions on UK travel include Hong Kong, Israel, Iran, Croatia, Argentina, Chile, Morocco and Kuwait.
