Dhaka: England has published a list of 50 countries for which quarantine will not apply to the travellers while they arrive in the country, effective July 10.
Countries including Greece, Spain, France and Belgium are on the list. But countries such as China, US, Sweden and Portugal are not, meaning arrivals from those have to self-isolate for 14 days.
Scotland and Wales are yet to decide whether to ease travel restrictions and described the changes as "shambolic".
The quarantine rules will also remain in place in Northern Ireland for visitors arriving from outside of the UK and Republic of Ireland.
The restrictions came into place in early June in a bid to stop coronavirus entering the country as the number of cases was falling.
Prime Minister Boris Johnson said, "Instead of quarantining arrivals from the whole world, we will only quarantine arrivals from those countries where the virus is sadly not under control."
People travelling from the 59 places and 14 British overseas territories on the list will not have to quarantine on arrival in England unless they have travelled through a place which is not exempt.
Passengers will still be required to provide contact information on arrival in England.
Some of those on the list include popular short-haul destinations such as Turkey and Cyprus, as well as long-haul locations including Australia, Barbados, Hong Kong, Japan, New Zealand and Vietnam.
However, some countries will require visitors to isolate on arrival or will bar them from entering at all, such as New Zealand.
The Foreign Office is expected to update its travel guidance on July 4, including naming which countries will have a reciprocal arrangement with the UK and not require British visitors to quarantine on arrival.
A list of countries which will be exempt from the Foreign Office's advice against "all but essential travel" from July 4 has also been published.
The advice has been lifted for Portugal but only for the Azores and Madeira.
The government said information for travel into Scotland, Wales and Northern Ireland will be published in due course by the devolved administrations.
Transport Secretary Grant Shapps said finalising the list of countries had been delayed - after scrapping the quarantine was announced last week - in the hope that the four UK nations could reach a joint decision.
He said there was "still an opportunity" for Scotland, Wales and Northern Ireland to co-ordinate and therefore make the changes more simple.
Johnson said in a televised coronavirus briefing from Downing Street that the nations of the UK were following "very similar paths but at different speeds".
The introduction of the quarantine on June 8 was met with criticism from the travel, tourism and hospitality industries and the easing of restrictions on arrivals from some countries has been welcomed.
A statement on behalf of airlines Ryanair, easyJet and British Airways said the move to quarantine people had been "irrational" and had seriously damaged the economy and industry.