Restrictions banning social gatherings of more than six people are now in effect, as Covid-19 cases keep rising.
The "rule of six" applies both indoors and outdoors in England and Scotland, and indoors only in Wales.
England's restrictions affect everyone, but children under 11 in Wales and under 12 in Scotland are exempt.
Crime Minister Kit Malthouse said people should report neighbours they suspect of hosting a gathering of seven or more people.
But some Tory MPs have urged No 10 to exempt young children in England and called for a debate over the rules.
The restrictions began after the UK's R number escalated to between 1 and 1.2 for the first time since March, indicating infections are rising.
A further 3,330 positive cases were recorded in the UK on Sunday - the third consecutive day with more than 3,000 - with five more deaths reported.
According to the UK government's coronavirus dashboard, the total number of reported coronavirus deaths across the UK is 41,628.
Mr Malthouse told BBC Radio 4's Today programme people should use the non-emergency contact number to report gatherings of seven or more to the police.
"If they are concerned and they do see that kind of thing then absolutely they should," he said.
The minister added that Covid-secure marshals - who could promote the new rules - had proved useful across the country during lockdown and "the intention is that we roll those out across the country".
At-a-glance: What are the new rules?
Social gatherings of more than six people in England, Scotland and Wales will not be allowed in law from Monday 14 September with some exceptions The new rule applies to people in private homes, indoors and outdoors, and places such as pubs, restaurants, cafes and public outdoor spaces In Scotland, the rule applies to a maximum of two households and in Wales it applies to the same extended household It applies to all ages in England, but not to those aged 12 and under in Scotland, and those under 11 in Wales The rule does not apply to schools and workplaces, or weddings, funerals and organised team sports A full list of exemptions has been published in England People who ignore police could be fined £100 - doubling with each offence to a maximum of £3,200National Police Chiefs' Council chairman Martin Hewitt told BBC Breakfast officers would continue to explain restrictions to people.
"We will carry on enforcing these in the same way we have been doing this for what's now nearly six months," he said.
"We're part of the group that are trying to explain to members of the public what the rules are and encouraging people to comply with them."
Home Secretary Priti Patel earlier urged the public not to break the rules and said "the recent rise in cases makes it clear that more needs to be done to stop the spread of this disease".
Under the new rules, larger gatherings are still allowed at gyms, schools, places of worship, weddings and funerals. Education and work settings are not affected.
The "rule of six" in England replaces the existing ban on gatherings of more than 30 people and the current guidance on allowing two households to meet indoors.
England, Scotland and Wales each have new restrictions, with several key similarities and differences.
Groups larger than six can be broken up by police, with members of the group facing fines of £100 for a first offence, doubling on each further offence up to £3,200.
Northern Ireland announced a six person, two household limit on indoor gatherings on 24 August, a reduction on a previous restriction of 10 people from four households.
The devolved nations have powers to set their own coronavirus restrictions, and while the UK nations have broadly moved in the same direction, they have done so at their own pace during the pandemic.
The Metropolitan Police said it will deploy resources across the capital to enforce the tighter restrictions on social gatherings.
But the West Yorkshire Police Federation, which represents rank-and-file officers, warned that staff are already so stretched that relying solely on the police to enforce the new law is unrealistic.
It came as a British Medical Association survey of 8,000 doctors and medical students suggested a second peak of Covid-19 is their number one concern.
Pub chain JD Wetherspoon insisted its venues were safe after it confirmed 66 of its workers had tested positive for coronavirus.
Meanwhile, people across England told BBC News they are struggling to access coronavirus tests, with dozens unable to book a swab.
THE RULE OF SIX: What's in the small print? UNWIND WITH THE MINDFUL MIX: Switch off and escapeHow will the new rules affect you? Do you have a question about them? If you have had a coronavirus test what was the process like? Tell us by emailing haveyoursay@bbc.co.uk.
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