The country's health secretary says two million of the most vulnerable people have been vaccinated, but people still needed to remain indoors.
People in Britain have been urged to avoid "flexing" coronavirus restrictions amid concerns that hospitals may soon be unable to cope.
A national lockdown is now in force as COVID-19 case numbers surge across the country, particularly in England.
Authorities announced on Sunday they had recorded 54,940 new cases of COVID-19 around the UK in the preceding 24 hours and 417,570 over the past week.
With the virus spreading fast, health officials have urged people to behave like they already have the virus and avoid trying to flex the rules.
"The challenge here is that every flex can be fatal," Health Secretary Matt Hancock said on Sunday.
"You might look at the rules like, well, it doesn't matter too much if I just do this or do that. But these rules are not there as boundaries to be pushed. They're the limit of what people should be doing".
The restrictions are in place to help curb the spread of a coronavirus variant that was first identified in the UK last month and is much more transmissible than earlier variants.
In an editorial for the Sunday Times newspaper, the country's chief medical officer Chris Whitty wrote it was "the most dangerous situation anyone can remember".
"We could be looking at 1 in 30 people carrying the new variant of COVID and often people are not symptomatic as well," said Dr Nikki Kanani, a director in England's health service.
"So it's more important than ever that we roll out this vaccination programme and get people protected".
Hancock said the UK's vaccine rollout was gathering pace and that it might be possible to end restrictions on movement sooner than the March 31 deadline set out in law.
Two million of the country's most vulnerable people have now been vaccinated.
But UK opposition leader Keir Starmer said that while he believed most British people were complying with the restrictions, they were having to contend with confusing directives from the government.
He said: "The problem has been the government's mixed messages: eat out, don't eat out, go back to work, don't go to work. Stay at home, don't stay at home. The central message now is critically important. Stay home, save lives, and protect our NHS".