There are more than 40 countries on the government's red list, which has the strictest travel restrictions.
One is India, where a new mutation of coronavirus first identified in the country has spread to the UK. This has been linked to international travel. It has been classified as a "variant of concern" and more than 3,400 cases of it have been found in the UK.
But despite this and the discovery in the UK of other variants identified abroad, the government has never banned international travel altogether - unlike some countries.
What are the current travel rules?
A traffic light system has been introduced for travel, with countries classed as green, amber or red - with different rules for quarantine and Covid tests.
Red list countries (which include India, Pakistan, Brazil and South Africa) are those the UK government says are at the highest risk from Covid, and should not be visited "except in the most extreme of circumstances".
If you have been in one, you can only enter the UK if you are a UK or Irish national, or UK resident.
You must be tested negative for Covid-19 before departure and self-isolate for 10 days in a government-approved quarantine hotel.
Direct flights from many red list countries to the UK are banned but some are allowed. These include flights from India, Pakistan, Bangladesh and Kenya. The government says this is to avoid potential disruption to critical freight and British nationals seeking to return home.
On one day (19 May), Reality Check counted 4 direct flights from India to Heathrow.