Travellers returning to the UK from mainland Greece, Iceland and Denmark could soon have to quarantine for two weeks on their return.
Greece, a popular summer holiday destination for Britons, is currently recording a seven-day rate of 20.5 Covid-19 cases per 100,000 people.
This is up from 17.7 a week ago.
A rate of 20 is the threshold above which officials consider removing countries from the government's quarantine-exemption list.
Iceland and Denmark are also at risk of having quarantine measures introduced, with case rates of 68.6 and 63.2 respectively, following rapid increases in recent days.
Other countries at or near the threshold include Sweden (20) and Italy (18.1).
Cyprus has seen its rate tick upwards to 8.9, compared with 3.3 a week ago.
The rates in the UK and Ireland are 44 and 38.6 respectively.
Earlier this month the government introduced a regional approach to its quarantine list which saw restrictions introduced for arrivals from seven Greek islands, but the rest of the country maintained its exemption.
Figures have been calculated by the PA news agency based on data collected by the European Centre for Disease Prevention and Control.
Changes to the government’s list of countries from which arrivals in England do not need to self-isolate for 14 days are usually announced on Thursday at 5pm and implemented the following Saturday at 4am.
The devolved nations have their own exemption lists which are similar but not identical to that created by the UK government.
The travel industry has been badly hit by quarantine restrictions.
It has called on the government to allow coronavirus testing at airports to reduce self-isolation periods for those who get a negative result.