The UK is to close all travel corridors from Monday morning to "protect against the risk of as yet unidentified new strains" of Covid, the PM has said.
Anyone flying into the country from overseas will have to show proof of a negative Covid test before setting off.
It comes as a ban on travellers from South America and Portugal came into force on Friday over concerns about a new variant identified in Brazil.
Boris Johnson said the new rules would be in place until at least 15 February.
A further 1,280 people with coronavirus have died in the UK within 28 days of a positive test, taking the total to 87,291.
The latest government figures on Friday also showed another 55,761 new cases had been reported - up from 48,682 the previous day.
Meanwhile, more than two million people around the world have now died from the virus since the pandemic began, according to figures from Johns Hopkins University.
Speaking at a Downing Street press conference, the prime minister said it was "vital" to take extra measures now "when day by day we are making such strides in protecting the population".
"It's precisely because we have the hope of that vaccine and the risk of new strains coming from overseas that we must take additional steps now to stop those strains from entering the country."
All travel corridors will close from 04:00 GMT on Monday. After that, arrivals to the UK will need to quarantine for up to 10 days, unless they test negative after five days.
Mr Johnson, who said the rules would apply across the UK after talks with the devolved administrations, added that the government would be stepping up enforcement at the border and in the country.
Travel corridors were introduced in the summer to allow people travelling from some countries with low numbers of Covid cases to come to the UK without having to quarantine on arrival.
Trade body Airlines UK said it supported the latest restrictions "on the assumption" that the government would remove them "when it is safe to do so".
Chief executive Tim Alderslade said travel corridors were "a lifeline for the industry" last summer but "things change and there's no doubting this is a serious health emergency".
Labour leader Sir Keir Starmer said it was the "right step" but called the timing of the decision "slow again", adding that the public would be thinking "why on earth didn't this happen before".
The prime minister warned that the NHS was facing "extraordinary pressures", having had the highest number of hospital admissions on a single day of the pandemic earlier this week.
He said that came on Tuesday when there were 4,134 new admissions, while the UK currently has more than 37,000 Covid patients in hospitals.
Mr Johnson said that once the most vulnerable have been vaccinated by mid-February "we will think about what steps we could take to lift the restrictions".
England is currently under a national lockdown, meaning people must stay at home and can go out only for limited reasons such as food shopping, exercise, or work if they cannot do so from home.
Similar measures are in place across much of Scotland, Wales and Northern Ireland.
Also speaking at the No 10 briefing, England's chief medical officer Prof Chris Whitty said the restrictions would need to be lifted gradually by "testing what works, and then if that works going the next step".
He said the peak of people entering hospital would be in the next week to 10 days for most places, but "we hope" the peak of infections "already has happened" in the south-east, east and London.
"The peak of deaths I fear is in the future, the peak of hospitalisations in some parts of the country may be around about now and beginning to come off the very, very top," he said.
'Easy' to adjust vaccines
A ban on travellers from South America, Portugal and Cape Verde entering the UK came into force on Friday morning as a result of a new, potentially more infectious variant of coronavirus linked to Brazil.
The government's chief scientific adviser Sir Patrick Vallance told the press briefing that some of the new variants may be able to "get round" the Covid vaccines but it was "really quite easy" to adjust the vaccines to deal with mutations in the virus.
New variants causing concern have previously been identified in the UK and South Africa, with many countries imposing restrictions on arrivals from both nations.
Public Health England said a total of 35 genomically confirmed and 12 genomically probable cases of the Covid-19 variant which originated in South Africa have been identified in the UK as of 14 January.
Earlier, a leading scientist said one of the two variants first detected in Brazil had been found in the UK - but not the variant that was causing concern.
"I think it is likely that the vaccine we have now is going to protect against the UK variant and is going to provide protection I suspect against the other variants as well," said Sir Patrick. "The question is to what degree."
Latest figures show that more than three million people in the UK have now received the first dose of a vaccine - 3,234,946 - an increase of 316,694 from the previous day.
Sir Patrick said he expected the vaccines would reduce transmission of the virus but that "we shouldn't go mad" as jabs are rolled out because a risk would remain.
"Just because you've been vaccinated doesn't mean you can't catch this and pass it on, it means you're protected against severe disease," he added.
Meanwhile, the latest estimate of the UK's R number - which is the number of people that one infected person will pass on a virus to on average - is 1.2 to 1.3, compared with 1-1.4 last week.
But in London, where tight restrictions came in earlier, the R number is lower - between 0.9 and 1.2.
In Wales, new laws for shoppers and staff are to be introduced after "significant evidence" coronavirus is being spread in supermarkets.
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