Travellers arriving in the UK from dozens of countries no longer have to self-isolate for two weeks from Friday.
The rules are being relaxed for arrivals from 75 countries and British overseas territories.
However, Scotland still requires people travelling from Spain to quarantine – unlike England, Wales and Northern Ireland.
The Foreign Office’s advice against taking a cruise holiday remains in place.
From Friday morning, people arriving in the UK from France, Italy, Belgium, Germany and dozens of other countries will no longer have to spend 14 days in quarantine.
But people who arrived from those countries at an earlier point in the last two weeks will still be expected to complete their period of isolation, the government said.
On Friday, the UK government changed its advice for Serbia, no longer allowing travellers to return without quarantining.
Scotland, which from Friday has also made face coverings mandatory in shops, has said it will continue to quarantine passengers from countries with a higher prevalence of Covid-19 than its own.
It means people arriving in Scotland from Spain will still face quarantine rules. The Scottish government said data from the UK government showed the prevalence of the virus in Spain is 330 people per 100,000, compared with 28 people per 100,000 in Scotland.
First Minister Nicola Sturgeon said the “difficult decision” was necessary to protect Scotland from a resurgence of the virus. She said travellers could not bypass the restrictions by flying to airports in England and sample checks would be carried out.
Among those setting off on holiday on Friday was Billy Marigold, who is flying with his family to Geneva from Gatwick Airport to celebrate his 60th birthday.
“It was only last week we made a decision,” he told BBC Breakfast.
“Even last week we were talking about whether we can go or not, because none of us can self-isolate for two weeks when we come back. And we were so worried about self-isolating on the other side as well.”
The quarantine rules were introduced in June, with travellers asked to nominate an address where they would self-isolate, with fines of up to £1,000 for those in England who failed to comply.
As some international travel to and from the UK is opened up, the Foreign Office is continuing to warn against journeys on cruise ships, however.
Warnings against cruise ship travel were first issued for over-70s in March before the Foreign Office began advising against all but essential travel.
A spokesman said the decision not to change the advice against cruises is based on “medical advice from Public Health England”, but it would “continue to review” the position.
Carnival, the world’s largest cruise company which owns P&O and Cunard, said it had already put its voyages on hold until the autumn and would not resume them until “rigorous protocols” were agreed with government and put in place. What are my holiday travel and insurance rights?
Will travel insurance cover me if I get coronavirus?
Where the Foreign Office advice states UK residents should not travel, it is very unlikely that any travel insurance will be valid.
For example, Foreign Office advice against taking a cruise holiday remains in place as it does for travel to a number of high-risk countries.