But how long will these bans last and is anyone exempt?
France, Germany, Italy, and Spain are among the major European countries to have halted flights from the UK.
France's ban includes the movement of freight driven between the two countries, but officials say they are "working on protocol" to allow movement from the UK to resume.
The Czech Republic has imposed stricter quarantine measures for people arriving from Britain but is yet to close the border to Brits.
European countries that have banned travel from the UK:
Where else have travel bans been implemented?
Beyond Europe, the number of countries closing their borders to the UK is increasing.
Turkey and Morocco have announced they will be suspending air travel from the UK.
Hong Kong is banning all flights arriving from the UK from midnight - and the quarantine of passengers who arrived from Britain in the last fortnight is being extended.
Canadian prime minister Justin Trudeau said from midnight Sunday, Canada was putting a 72-hour stop on flights from the UK.
India will ban all flights from midnight on December 22 until the end of the year.
Iran's health ministry has ordered flights suspended for two weeks, according to state news agency IRNA.
Israel has announced it will ban entry for foreign citizens travelling from Britain, Denmark and South Africa.
Saudi Arabia announced on Sunday it was halting all travel into the country - via flight, land, and sea - for at least a week.
Flights from the UK into Kuwait have been banned after Britain was added to a list of "high-risk" nations.
El Salvador and Argentina both announced on Sunday they would be closing their borders to incoming flights from the UK,
While Chile's flight ban comes into force from Tuesday.
Morocco banned all flights to the UK from Sunday.
Are international train and ferry links running?
Eurostar said it was unable to run trains from London to Paris, Brussels, Lille or Amsterdam on Monday or Tuesday.
Trains to London from Paris will continue to operate, with the rail company saying it planned to resume services to and from the UK on Wednesday.
Eurotunnel said access to its UK site was prohibited from 10pm after its last train left at 9.34pm.
Dover’s ferry terminal has also closed to “all accompanied traffic leaving the UK” after France moved to shut its border.
When do the travel bans start and how long do they last?
The Netherlands ban came into force on Sunday morning, with it due to last for at least the rest of the year.
Belgium’s prime minister Alexander De Croo issued a flight ban order for 24 hours starting at midnight on Sunday.
Italy’s health minister Roberto Speranza said an order was signed on Sunday blocking flights from Britain and preventing anyone who had been to the UK in the last 14 days from entering Italy. The order bans plane travel until January 6.
Austria’s ban on flights from the UK starts at midnight on December 22 and anyone arriving in the country before that date must quarantine for 10 days. It is unclear how long the ban will last.
Germany said it was banning flights from the UK starting at midnight, Berlin time, on Sunday, with the German dpa news agency reporting it would remain in place until at least December 31.
France has banned all travel from the UK for 48 hours from midnight on Sunday.
Bulgaria said it was temporarily ceasing flights to and from the UK from midnight on Sunday. Finland is due to suspend all passenger flights with the UK for two weeks from Monday.
Poland is also due to halt flights from midnight on Monday, though it is not yet known how long the ban will be in place.
While Denmark said all flights from Great Britain would be halted for 48 hours from Monday.
What is the situation with Ireland?
The Irish Government said on Sunday that it was imposing a 48-hour ban on flights from Britain to Ireland.
The restrictions come into force at midnight on Sunday.
Is anyone exempt from the bans?
Ireland’s transport minister Eamon Ryan said ferries will continue to operate for freight between Britain and Ireland.
“We need haulage coming in to keep our shelves full but other passengers will be restricted,” he said.
The German government said exemptions from its flight ban include repatriation flights of planes and their crews, postal, freight or empty flights and aircraft carrying medical personnel.
The Bulgarian embassy in London said on its website that Bulgarian citizens and their families, as well as permanent residents in Bulgaria, were able to enter the country subject to a 10-day quarantine if they fly through a different country or enter Bulgaria on land or by sea.
Why is this all happening?
A mutant strain of coronavirus sweeping across London and the South East of England has prompted the EU nations to start restricting inbound flights from the UK.
Mr De Croo said Belgium’s flight ban was “out of precaution”, adding: “There are a great many questions about this new mutation and if it is not already on the mainland.”
The German embassy in London tweeted that flight restrictions were the result of “the coronavirus mutation”.
On Saturday, Prime Minister Boris Johnson said there was “no evidence” the new variant “causes more severe illness or higher mortality” but “it does appear to be passed on significantly more easily”.
He said the new strain could be up to 70% more transmissible than the old virus variant.
What discussions are taking place between governments?
An EU crisis meeting has been called for Monday to discuss the coordination of the response to coronavirus among the 27 member states.
The UK’s Foreign, Commonwealth and Development Office (FCDO) regards other countries’ travel restrictions as a matter for their own governments.
It was previously understood to be in touch with international partners and monitoring the situation closely.
But late on Sunday night No 10 revealed that Boris Johnson is due to chair a meeting of the UK government’s Cobra civil contingencies committee on Monday.
Am I allowed to travel abroad from England?
If you are living in one of the newly created Tier 4 areas, which encompasses London and parts of the south east and east of England, you must not travel abroad.
Government guidance states people can only travel internationally if you are “legally permitted to do so, for example, because it is for work”.
Across England people are advised to stay local and avoid travelling outside their area.
For those living in Tier 1, 2, and 3 areas, the guidance advises potential international travellers to “carefully consider whether they must travel abroad”.
It advises them to “follow the rules in their area” and consider the public health advice in the country they plan to visit.
Someone living outside Tier 4 can transit into or through a Tier 4 area to travel abroad if they need to.
People are also warned to check travel advice from the Foreign, Commonwealth and Development Office (FCDO) and what rules are in place at their destination. For many countries the FCDO is advising against “all but essential travel”.