Amid reports that foreign holiday destinations "will be graded using a traffic light system" based on how well they are coping with the pandemic.
Some travellers forced to self-isolate after arriving from "red list" countries are not happy.
The transport secretary said the number of people coming from the 33 "red list" countries was "less than 1,000 people a day".
Health secretary says the new border rules will come into force from Monday.
Keir Starmer has accused the government of causing "chaos and confusion".
Transport secretary defended the government's record on border controls.
Anyone arriving in the UK from 30 Covid hotspots will soon have to quarantine in hotels. Scientists have been suggesting it since April.
UK residents will be required to follow the new rule. People leaving the country will also have to prove they have a "valid" reason.
But Boris Johnson has been accused of acting too slowly to prevent new variant of coronavirus from being imported.
So far ten European countries have closed borders to Britain amid fears about a new strain of the coronavirus ahead of Christmas week. A mutant strain sweeping across London and the South-East of England has prompted EU nations to start restricting inbound flights from the UK. British Prime Minister Boris Johnson said there is no evidence the new variant causes more severe illness or higher mortality but it does appear to be passed on significantly more easily. He said the new strain could be up to 70% more transmissible than the old virus variant.