London and large swathes of south-east England were placed in the highest tier four restrictions over the weekend.
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Nations including Germany, Italy, Belgium, the Irish Republic, Turkey and Canada are suspending UK flights.
The Port of Dover is closed to traffic leaving the UK “until further notice” due to border restrictions in France, port authorities said in a statement.
Covid-19: Christmas rules tightened for England, Scotland and Wales
Christmas rules tightened for millions The relaxation of rules for mixing is cut from five days to Christmas Day in England, Scotland and Wales – and scrapped completely for much of south-east England.
But analysis suggests the R number – which represents how many people each infected person passes the virus onto – has risen above 1 in the UK.
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Northern Ireland will begin a six-week lockdown from 26 December, with non-essential shops having to close.
What happens next with Brexit?
On Wednesday, London and parts of Essex and Hertfordshire moved to tier three amid a rise in infection rates.
BBC political editor Laura Kuenssberg said similar, tougher advice was expected to be announced for England.
It comes as London, much of Essex and parts of Hertfordshire moved into tier three restrictions overnight.
It came after two leading medical journals described the rules as “rash”.
Schools can remain open, but the government has threatened legal action against Greenwich Council, in south-east London, after it wrote to head teachers asking all schools to move classes online amid a rise in Covid cases.
Read more about the tier three rules
Tens of thousands of people in the UK received the Pfizer-BioNTech jab last week in hospitals.