People in all of England and most of Scotland must now stay at home except for a handful of permitted reasons, as new lockdowns begin in both nations.
Schools have closed to most pupils in England, Scotland and Wales, while Northern Ireland will have an “extended period of remote learning”.
England’s rules are due to last until at least mid-February; Scotland’s will be reviewed at the end of January.
PM Boris Johnson warned the coming weeks would be the “hardest yet”.
Cabinet Office Minister Michael Gove said the chancellor will give more details later about additional support for businesses and the education secretary is due to make a statement in the House of Commons on Wednesday on “how we want to make sure children are fairly assessed”.
It comes after the UK reported a record 58,784 cases on Monday, as well as a further 407 deaths within 28 days of a positive test.
Announcing England’s lockdown, Mr Johnson said hospitals were under “more pressure from Covid than at any time since the start of the pandemic”.
He ordered people to stay indoors other than for limited exceptions – such as essential medical needs, food shopping, exercise and work that cannot be done at home – and said schools and colleges should move to remote teaching for the majority of students until at least half term.
And he said all care home residents and their carers, everyone aged 70 and over, all frontline health and social care workers, and the clinically extremely vulnerable will be offered one dose of a vaccine by mid-February.
While the rules become law in the early hours of Wednesday, people should follow them now, the PM added.
Earlier on Monday, First Minister Nicola Sturgeon issued a stay-at-home order for Scotland, beginning at midnight and lasting until the end of January.
Scotland’s lockdown, which is for the mainland and Skye, will also see schools closed to pupils, places of worship closed and group exercise banned.
“It is no exaggeration to say that I am more concerned about the situation we face now than I have been at any time since March last year,” Ms Sturgeon said.
Wales, which has been in a national lockdown since 20 December, said schools and colleges would shut until 18 January for most pupils.
Meanwhile, Northern Ireland, which entered a six-week lockdown on 26 December plans to put its stay-at-home message into law, and will have an “extended period of remote learning”, the Stormont Executive said.
And in England, exams will again face disruption. The prime minister said they would not take place as normal in the summer, while a government source told BBC News that A-Levels and GCSEs will be cancelled.
‘Will save lives’
“The more we vaccinate the easier it will be to lift these restrictions,” Mr Gove told BBC Breakfast, saying a million people had been vaccinated so far “up until the weekend” and they hope the number will reach more than 13 million in February.
When asked about the target of two million vaccines a week and concerns over logistics and the safety systems, he said: “We do want to make sure these vaccines are delivered in the safest possible way that we do not waste a drop.
“The process of making sure that the vaccines can be placed in the appropriate vials and then safely injected into people’s arms is a complicated exercise, but the NHS has more than risen to the challenge.”
He added that the government was “looking at further options” to restrict international travel.
Prof Andrew Hayward – a member of the government’s Scientific Advisory Group for Emergencies (Sage) – told BBC Radio 4’s Today programme the lockdown measures “will save tens of thousands of lives”.
But he said “the virus is different” and “it may be that the lockdown measures that we have are not enough”
“This lockdown period we need to do more than just stay at home, wait for the vaccine, we need to be actively bearing down on it,” he said.
Under England’s new measures, support and childcare bubbles will continue, and people can meet one person from another household for outdoor exercise.
Exercise should be limited to once per day.
Communal worship and funerals can continue, subject to limits on attendance. Weddings are allowed in “exceptional circumstances” with up to six people.
Mr Johnson said the new variant of coronavirus, which is up to 70% more transmissible, was spreading in a “frustrating and alarming” manner and warned that the number of Covid-19 patients in English hospitals is 40% higher than the first peak.
He added, however, that vaccinating the top four priority groups by mid-February could allow restrictions to be eased.
People who are clinically extremely vulnerable will be contacted by letter and should now shield once more, Mr Johnson said.
The House of Commons has been recalled to allow MPs to vote on England’s new restrictions on Wednesday.
Labour leader Sir Keir Starmer said his MPs would “support the package of measures”, saying “we’ve all got to pull together now to make this work”.
But business leaders have expressed concern over the level of financial support.
British Chambers of Commerce director general Adam Marshall said companies would understand why a lockdown was necessary – but added they will be “baffled and disappointed… that he did not announce additional support for affected businesses alongside these new restrictions”.
Mr Johnson spoke after UK chief medical officers recommended the Covid threat level be increased to five – its highest level.
Level five means the NHS may soon be unable to handle a further sustained rise in cases, the medical officers said in a joint statement.
Chris Hopson, chief executive of NHS Providers, which represents health service trusts, said patients were being admitted to hospital at an “alarming rate” and that “immediate and decisive action” was needed.