People are being warned they should not be mixing with other households indoors and that they should avoid large gatherings of any kind.
Health Secretary Matt Hancock said people “cannot let up” now in the fight against the virus, with the health service under strain from increasing numbers of Covid-19 patients.
A Government advertising campaign to “See in the New Year safely at home” is running throughout Thursday, reminding people of the virus’s easy spread and that around one in three people who have the infection have no symptoms and so could pass it on without realising.
Mr Hancock said: “With our NHS under pressure we must all take personal responsibility this New Year’s Eve and stay at home.
“I know how much we have all sacrificed this year and we cannot let up. Over 600,000 people have now been vaccinated and we are close to beating this virus.
“Now more than ever, we need to pull together to save lives and protect our NHS. If we continue to do our bit by staying at home, we can get through this together.”
At a Downing Street press conference on Wednesday, Professor Stephen Powis, NHS England’s national medical director, reminded people that “Covid loves a crowd” as he urged them not to mix outside their household or support bubble.
He said staying at home and seeing in 2021 “within the rules” will reduce infections and relieve pressure on hospitals.
He told the briefing: “We know it’s the end of the year, it’s a time where people traditionally want to celebrate.
“But it’s absolutely vital that this year, everybody continues to follow the guidance by staying at home and not mixing.”
Prof Powis added: “We can all play a part in fighting this terrible virus: stay at home, mark the New Year with just nearest and dearest within the rules.
“This action will reduce infections, relieve pressures on hospitals, and that’s how everybody can help to save a life.
“Covid loves a crowd, so please leave the parties for later in the year.”
His call for restraint came as deputy chief medical officer Professor Jonathan Van-Tam said the NHS had yet to see the impact of household mixing over Christmas.
He said the situation in the UK is “precarious in many parts already” and urged the public to “play your part from bringing us back from this very dangerous situation”.
“It is almost certainly true that the NHS has not yet seen the impact of the infections that will have occurred during mixing on Christmas Day and that is also unfortunately rather sobering,” Prof Van-Tam said.
Prime Minister Boris Johnson also urged people to follow the rules on December 31.
He said: “I must ask you to follow the rules where you live tomorrow night and see in the New Year safely at home.
“That means not meeting up with friends or family indoors, unless they’re in the same household or support bubble, and avoiding large gatherings of any kind.”
The Metropolitan Police issued a warning to potential revellers to “celebrate the New Year in the comfort of their own homes, not the homes of family and friends”.
Commander Paul Brogden, who is leading this year’s operation, said the public should expect to see officers deployed across the capital “supporting communities and focusing strongly on the few people intent on breaching and ignoring the guidance put in place to keep everyone safe”.
He said officers will be strongly encouraging those who might be planning events to cancel them, and warned fines will be issued for rule-breakers.
He said: “If people insist on gathering and breaching regulations, then officers will attend and encourage people to disperse.
“Where necessary, enforcement action, including fines starting at £100 and working their way up to £10,000, will be considered.”