Prime Minister Boris Johnson has called on the public to "summon the discipline and the resolve" to follow the new coronavirus rules announced on Tuesday.
In a television broadcast to the country he warned the government may go further if people do not stick to them.
Mr Johnson said while the vast majority have complied with the measures so far, "there have been too many breaches".
New restrictions were announced across the UK earlier, with Mr Johnson warning rules could last for up to six months.
In England, rules on face coverings have been expanded and the number of people allowed at weddings has been halved.
Pubs, restaurants and other hospitality venues will have to close by 22:00 BST, while the fines for breaking the rules will also increase to £200 on the first offence.
Hospitality venues will also have to close early in Scotland and Wales – but Scotland has gone further, banning people from visiting other people's homes. Northern Ireland has also already banned households mixing indoors.
It comes as the number of UK cases rose by 4,926 on Tuesday, government figures showed, with deaths increasing by 37.
'Can't just lock up elderly'
Speaking on Tuesday evening, Mr Johnson explained the new measures, saying they were "robust but proportionate".
"And to those who say we don't need this stuff, and we should leave people to take their own risks, I say these risks are not our own," he said.
"The tragic reality of having Covid is that your mild cough can be someone else's death knell.
"And as for the suggestion that we should simply lock up the elderly and the vulnerable – with all the suffering that would entail – I must tell you that this is just not realistic, because if you let the virus rip through the rest of the population it would inevitably find its way through to the elderly as well, and in much greater numbers."
Mr Johnson said he was "deeply, spiritually reluctant" to infringe on anyone's freedom, but added: "Unless we take action the risk is that we will have to go for tougher measures later."
"If people don't follow the rules we have set out, then we must reserve the right to go further," he added.
More police will be put on the streets and the Army will be used as back-up if need be, he said.
"If we follow these simple rules together, we will get through this winter together," he added. "There are unquestionably difficult months to come.
"And the fight against Covid is by no means over. I have no doubt, however, that there are great days ahead.
"But now is the time for us all to summon the discipline, and the resolve, and the spirit of togetherness that will carry us through."
In her statement on Tuesday evening, Scottish First Minister Nicola Sturgeon said: "In a global pandemic of a virus with as yet no vaccine, we simply can't have 100% normality. No country can. So we must choose our priorities."
She said that although "today must feel like a step backwards", the country is "in a much stronger position than in the spring".
"It won't last forever and one day, hopefully soon, we will be looking back on it, not living through it," she said.
And she added: "I will never find the words to thank all of you enough for the enormous sacrifices you have made so far. And I am sorry to be asking for more."
Meanwhile, Wales' First Minister Mark Drakeford said: "In the weeks and months ahead of us, there is a very real possibility we could see coronavirus regain a foothold in our local communities, towns and cities. None of us wants to see that happen again".
Earlier, Mr Johnson told MPs that the new rules were "carefully judged" to achieve the maximum reduction in the R number – which measures how quickly the virus is spreading – while causing "the minimum damage to lives and livelihoods".
If these restrictions fail to bring the R number below one – the point where the epidemic is no longer growing – "then we reserve the right to deploy greater fire power with significantly greater restrictions" he said.
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Mr Johnson said that unless progress was made, people should assume the restrictions would remain in place "for perhaps six months".
But Ms Sturgeon said the rules in Scotland would "not necessarily" be in place for as long as six months – and would be reviewed every three weeks.
Labour's shadow health secretary Jonathan Ashworth told the BBC the new restrictions could have been avoided if the government "fixed testing and tracing".
Mr Ashworth said Labour supported the new measures but that "we shouldn't have been here".
"So what we need to do now is drive infections down, we all need to follow the rules, but the government in return have really got to fix this testing system and this tracing system, and give people the support when they need to isolate."
What are the new rules?