Home Secretary Priti Patel has said officers "will not hesitate" to enforce lockdown rules as she defended the way police have handled breaches.
She said rising numbers of coronavirus cases and deaths illustrated the need for "strong enforcement".
It comes after the National Police Chiefs' Council published guidance saying officers should issue fines more quickly when rules are broken.
More than 30,000 fines have been handed out by forces in England and Wales.
NPCC figures show 32,329 fixed penalty notices were issued between 27 March and 21 December last year.
The number of people who have died in the UK within 28 days of a positive Covid test surpassed 80,000 on Saturday, and a further 59,937 people tested positive.
Ministers have launched a new campaign urging people to act like they have the virus and scientists have warned that lockdown measures in England need to be stricter.
"The vast majority of the public have supported this huge national effort and followed the rules," Ms Patel said.
"But the tragic number of new cases and deaths this week shows there is still a need for strong enforcement where people are clearly breaking these rules to ensure we safeguard our country's recovery from this deadly virus.
"Enforcing these rules saves lives. It is as simple as that. Officers will continue to engage with the public across the country and will not hesitate to take action when necessary."
Health Secretary Matt Hancock has warned the public to follow the lockdown restrictions, telling the BBC's Andrew Marr programme that "every time you try to flex the rules, that could be fatal".
But Labour leader Sir Keir Starmer criticised the government for not providing "absolute clarity of messaging", telling the BBC's Andrew Marr that there had been "mixed messaging over the last nine months".
NPCC guidance, published on 6 January, says officers should still offer people "encouragement" to comply with the regulations and explain any changes.
"However, if the individual or group does not respond appropriately, then enforcement can follow without repeated attempts to encourage people to comply with the law," the NPCC said.
On Saturday 12 people were arrested during an anti-lockdown protest in south London.
Elsewhere, North Wales Police turned away more than 100 cars at Moel Famau in Flintshire by Saturday lunchtime, and Norfolk Police fined one couple who had travelled about 130 miles (209km) to see a seal colony.
However, Derbyshire Police has launched an urgent review into how fines were issued after two women were charged £200 each.
The pair were stopped by officers for walking five miles from their home with hot drinks, which they were told were not allowed as they were "classed as a picnic".
John Apter, chair of the Police Federation of England and Wales, said officers were under "immense pressure to do the right thing" and said with "such a changing landscape politically and legally" there were going to be things which did not go right.
He said the police had to balance the relationship with the public.
"It's not easy because all we are trying to do in policing is keep as many people safe as possible," he said.