Freight drivers who are not UK citizens and have been through Denmark in the last fortnight are warned they will be turned away from the British border.
It follows concern over a new coronavirus strain that has spread from mink to humans.
Returning drivers who are UK citizens will have to self-isolate for 14 days along with their households.
The new rules, which began at 04:00 GMT on Sunday, follow a ban on non-UK citizens coming to the UK from Denmark.
Any UK citizens who have travelled to Denmark must isolate for 14 days, along with their household.
Passenger planes and ships carrying freight from Denmark will also not be allowed to dock at English ports.
Cabin crew are also no longer exempt from the quarantine rules – which Ryanair described on Saturday as a “bizarre and baseless” move.
The airline said it had cancelled all flights to and from Denmark while the rules remain in place, and urged Mr Shapps to reverse the decision. Scottish airline Loganair said it has suspended flights between Scotland and Denmark from 9 to 22 November.
The Department for Transport (DfT) said the latest rules followed the release of “further information” from health officials in Denmark, where some 200 people have been found to have mink-related mutations of virus, most of them connected to farms in the North Jutland region.
The travel ban and extra requirements will be reviewed after a week, the DfT has said.
Asked about the restrictions by the BBC’s Andrew Marr, Foreign Secretary Dominic Raab denied the suggestion they were “draconian”, insisting the government had taken “safe and responsible steps” in light of the “new and evolving” science on the mutated virus strain.
He told the Andrew Marr show: “I wouldn’t describe it as draconian taking a precautionary measure that if and when we come up with a vaccine it can’t be sidestepped by a mutation in the virus that the Danes have found through their mink population.
“I think that’s a common sense measure that the public would expect us to take.”
Denmark is the UK’s largest source of imported pork – including bacon – with machinery among the other major import items.
A mutated strain of coronavirus that has spread to humans has triggered culls of millions of mink across Denmark and a lockdown in some parts of the country.
More than 200 people have been infected with strains related to mink, according to reports.
Mink kept in large numbers on farms have caught the virus from infected workers. And, in a small number of cases, the virus has crossed back from mink to humans, picking up genetic changes on the way.
Mutations in some of the strains, which have infected a small number of people, are reported to involve the spike protein of the virus, which is targeted by some, but not all, vaccines being developed.
The coronavirus, like all viruses, mutates over time, but there is no evidence that any of the mutations pose an increased danger to people.
The World Health Organization has said it is too early to jump to conclusions.
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In England, where a new national lockdown came into force on Thursday, people are still allowed to travel overseas for work or education trips.
Leaving home to go on holiday is currently banned for most people in the UK.
Denmark’s Minister of Foreign Affairs Jeppe Kofod called Mr Shapps’ travel announcement a “very drastic step” and said he had discussed it with UK Foreign Secretary Dominic Raab on Saturday.
Denmark had been taken off the UK coronavirus travel corridors list on Friday after it first became apparent the mutated form of coronavirus was present in the country. It meant any passengers arriving in the UK from Denmark would need to self-isolate after their arrival.
The Department for Health and Social Care estimates that between 300 and 500 people have arrived in the UK from Denmark in the last 14 days.
Officials will contact anyone in the UK who has been in Denmark in the last fortnight to make sure they also self-isolate.
Meanwhile, on Saturday, a further 413 people in the UK were reported to have died within 28 days of a positive coronavirus test, according to the latest daily figures from the government. It brings the overall UK death toll, by this measure, to 48,888.
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