Moving means people arriving from Switzerland, Czech Republic and Jamaica should self-isolate for 14 days to slow the spread of coronavirus.
The UK government has said that countries with a weekly infection rate above 20 per 100,000 are of particular concern when deciding to update the list.
Iceland could be the next country to be added on that basis, as figures show the country recorded 16.5 cases per 100,000 in the week of August 17-23.
Arrivals from tourist hotspots in Portugal and Greece could also be subject to the measure, according to figures from the European Center for Disease Prevention and Control (ECDC).
Data shows Greece had a weekly infection rate of 14.2 per 100,000 population in the week to August 23.
ECDC figures suggest that the number of daily infections has increased rapidly in Greece. The country had 65 cases on July 31 but that number had risen to 293 on August 27.
Portugal recorded a slightly higher infection rate of 14.3 per 100,000 population the week before 23 August.
Ireland has a higher rate than Greece and Portugal with 14.6 per 100,000 inhabitants.
Poland has the fifth highest rate of those not on the quarantine list with 13.4 cases per 100,000.
Switzerland had a weekly infection rate of 19.8 cases per 100,000 before being added to the list.
The Czech Republic had a weekly infection rate of 17.8 per 100,000 population.
Iceland, Ireland, Portugal and Greece therefore appear to be the countries most likely to join the tourist destinations of Spain and France on the quarantine list.
However, the number of infections in these countries is still much lower than that of Spain, which had 92.1 cases per 100,000, and France, which had 33.5 per 100,000.
Turkey had a rate of 10.9 cases per 100,000, meaning there would be more or less double the number of infections for it to be added to the list.
Germany, with 10.4 cases per 100,000, Cyprus, with 9.7 cases, and Italy with 7.8, also seem immune to being added to the list.
Sweden remains on the UK’s quarantine list despite a drop in cases of around 10%, from 19.3 per 100,000 to 17.3.
Serbia also remains on the list despite a drop in cases from 23.1 per 100,000 to 15.5 per 100,000.
The cases with the lowest infection rates in Europe are Finland with 2.7 per 100,000, Hungary with 2.6 per 100,000 and Latvia with 0.9 per 100,000.
The following countries are on the UK quarantine list:
Bosnia and Herzegovina
Trinidad and Tobago
Turks and Caicos Islands