Travellers in Switzerland, Jamaica and Czech Republic who return to the UK from 04:00 on Saturday are to be required to self-isolate for two weeks.
The UK government said the move was needed to keep UK infection rates down.
People arriving in Scotland from Switzerland are already required to self-isolate.
Cuba, where there has been a drop in cases, will be added to the list of destinations people can return from without entering quarantine.
The UK considers imposing quarantine conditions when a country’s rate of infection exceeds 20 cases per 100,000 people over seven days.
The government said there has been a “consistent increase” in the weekly case rate in Switzerland over the past four weeks, with cases per 100,000 rising from 18.5 to 22 over the past week.
Over 1.6m Britons travelled to Switzerland last year, the Swiss Tourism Federation estimated, drawn by the Alps and the mountain air.
The Czech Republic sees more than 300,000 British tourists every year, according to the Foreign and Commonwealth Office. The capital Prague is a popular destination for city breaks and stag dos.
Katarina Hobbs, director of CzechTourism UK and Ireland, insists the country “remains a safe country to travel to”.
“This is a British government decision that we deeply regret,” she said, adding she hoped they would reconsider it “very soon”.
The Foreign Office is now advising against all but essential travel to the Czech Republic, Jamaica and Switzerland.
UK tourists already in those countries are being told to “follow the local rules and check the FCO travel advice pages”.
In a tweet, Transport Secretary Grant Shapps warned British holidaymakers to “only travel if you are content to unexpectedly 14-day quarantine on return”.
There had been concern about a rising number of Covid cases in Gibraltar, but it remains on the UK’s quarantine exemption list.
In July, thousands of guests sat at a 500 metre-long (1,640ft) table on the Charles Bridge in Prague sharing food and drink at a party held to give the coronavirus a “symbolic farewell”.
The event’s organiser said the celebration in the Czech Republic capital was possible due to a lack of tourists in the famously charming city.
In Switzerland, a state of emergency was declared in March, with the government ordering the closure of schools, restaurants, bars and all the ski slopes.
But by June, as cases of Covid-19 started to fall across Europe and more travel was permitted, it reopened its mountain railways and cable cars.
Quarantine rules are set by each UK nation separately, but the DfT said equivalent measures are being put in place in Northern Ireland, Scotland and Wales.
Wales has made one further change – adding Singapore to the list of exemptions.
Last week restrictions were lifted on those returning from Portugal, but added for travellers coming back from Croatia, Austria and Trinidad and Tobago.
In July, travellers returning to the UK from Spain were caught out by the government’s decision to advise against all but non-essential travel to the mainland and islands after a spike in cases in the country.
And two weeks ago, visitors to France were given a few days’ notice that they would face a quarantine on their return home to the UK.
There has been widespread criticism of the government’s weekly reviews of travel restrictions.
The editor of Which? Travel, Rory Boland, said many holidaymakers found themselves “held to ransom” by airlines when trying to purchase new flights to beat the quarantine deadlines.
He called for greater transparency from the government so people had the necessary information in advance to decide whether it is safe to travel.
“Struggling tour operators can offer them trips to alternative destinations, rather than facing the financial hit of yet more cancellations and refund pay-outs,” he added.
Meanwhile, airport operator the Manchester Airport Group has called for an end to the UK’s “sluggish, illogical and chaotic” approach to quarantine.
The company’s chief strategy officer, Tim Hawkins, said the government has “essentially assumed control of the UK aviation industry”.
“These decisions aren’t being made anywhere near quick enough,” he said, adding that the industry could not be sustained with the “current outlook”.
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