A two-week quarantine period for anyone arriving in the UK is now being enforced.
Home Secretary Priti Patel said the move is to protect public health, because imported coronavirus cases ''pose a more significant threat''.
What are the new quarantine rules?
Passengers arriving in the UK by plane, ferry or train - including UK nationals - will be asked to provide an address where they will self-isolate for 14 days. Travellers can be fined £100 for failing to fill in a form with these details.
Surprise visits will be used to check they are following the rules. Those in England could be fined up to £1,000 if they fail to self-isolate.
Passengers should drive their own car to their destination, where possible. If they don't provide an address, the government will arrange accommodation at the traveller's expense.
Once at their destination they must not use public transport or taxis. They must not go to work, school, or public areas, or have visitors except for essential support.
They are also not allowed to go out to buy food, or other essentials, where they can rely on others.
People returning from overseas will not be automatically eligible for statutory sick pay unless they meet the required conditions - for example displaying coronavirus symptoms.
Is anywhere exempt from quarantine?
Anyone arriving from the Common Travel Area (CTA) - the Republic of Ireland, the Channel Islands, or the Isle of Man - will not have to enter quarantine, as long as they have been in the CTA for at least 14 days.
The government has also said it is looking into international travel corridors or "air bridges" to countries with low infection rates and strong healthcare systems. It hopes this could avoid the need for quarantine for travellers between the two.
Negotiations are already taking place between the UK and Portugal.
However, the government is currently advising against all non-essential travel abroad, and hasn't given a date for when quarantine will end.
The measures will be reviewed in late June, three weeks after their introduction, to check they remain ''effective and necessary''.
Who is exempt from quarantine?
There are a number of groups who are exempt, including:
Road haulage and freight workers
Medical and care professionals providing essential healthcare
Seasonal agricultural workers if they self-isolate where they are working
UK residents who ordinarily travel overseas at least once a week for work
Do other countries have quarantine rules?
Travellers could find they also have to enter quarantine when they arrive in another country. Some have introduced screening measures such as temperature checks, and entry restrictions.
From 21 June, Spain will re-open its borders to UK visitors, although the Spanish government has still to decide whether arrivals will need to quarantine
UK visitors to France are being asked to go into voluntary quarantine for 14 days after arrival
The US has barred entry to arrivals from the UK, with the exception of US citizens, their family members and "individuals who meet specified exceptions"
The United Arab Emirates has strict entry rules for foreign residents
UK citizens need a special exemption visa to travel to Australia
What has the response been?
Quarantine has not been welcomed by the UK's travel industry.
Airlines UK, which represents various airlines, said quarantine "would effectively kill off air travel".
British Airways, EasyJet and Ryanair have launched a legal challenge against the policy.
The British Ports Association, which represents ferry companies, has also spoken out against the measures - calling them "overzealous".
Will airlines still be flying?
EasyJet has restarted a limited number of flights to European destinations, with all passengers and cabin crew told to wear face masks.
Ryanair plans to reintroduce 40% of its flights from 1 July, subject to travel restrictions being lifted and safety measures being brought in at airports.
British Airways is reviewing its plans to run 50% of its schedule from July, because of the quarantine rules.