People arriving in the UK from mainland Greece will need to self-isolate for two weeks from 04:00 on Saturday, the transport secretary has said.
The rules will not apply to the Greek islands of Corfu, Crete, Rhodes, Kos and Zakynthos, Grant Shapps said.
Travellers from Qatar, the UAE, Laos and the Turks and Caicos Islands will no longer need to quarantine.
Bahrain, Chile, Iceland and Cambodia will also be exempt from isolation rules.
The Department for Transport (DfT) said data had shown “a consistent increase” in newly reported cases in Greece over the past fortnight, with a 136% increase in new cases to 16,429 between 5 and 12 November from 6,965 between 22 and 29 October.
It added the islands of Corfu, Crete, Rhodes, Zakynthos and Kos had not seen as significant a growth in cases over recent weeks as the rest of Greece and therefore quarantining was not required.
The UAE, Qatar, Turks & Caicos islands, Laos, Iceland, Cambodia, Chile and Bahrain were also seen as “posing a lower infection risk”, a statement said.
Denmark was cut from the UK’s safe list last week after a mutated strain of Covid-19 was found to have spread to humans from mink.
UK citizens can return from the country – but will have to isolate along with all members of their household for 14 days.
Current restrictions in England mean that only people with valid reasons are supposed to travel abroad at the moment.
People who break the rules face fines starting at £200 and rising to a maximum of £6,400.
In Wales, travel abroad is only permitted for people with a reasonable excuse.
England’s Nations League match against Iceland will be played at Wembley on Wednesday after a government exemption was granted for Iceland’s football team.
Iceland play Denmark in Copenhagen three days before that fixture – and there is currently a ban on entry to the UK for foreign visitors who have travelled directly or indirectly from Denmark.
But the “temporary and extremely limited exemption” was agreed, providing the Icelanders follow the strict medical protocols, introduced in June, that allow elite sporting teams to travel around the continent.
Meanwhile, the transport secretary said earlier this week that the UK is making “good progress” in developing a testing regime to reduce the amount of time people need to spend self-isolating.
He has previously said he is “very hopeful” a new testing regime for travellers to the UK could be in place by 1 December.
It is the highest daily figure since mass testing began in the UK, and brings the total number of cases to more than 1.29 million.