"We face a choice. If everybody follows the rules -- and we'll be increasingly stringent on the people who are not following the rules -- then we can avoid further national lockdowns," said the health secretary.
"I don't want to see more measures, more restrictive measures, but if people don't follow the rules that are how the virus spreads," he said, adding, "But we of course have to be prepared to take action if that is what is necessary."
Matt Hancock went on saying, "We’ll support people who do the right thing and we’ll come down hard on people who do the wrong thing."
The government has announced fines of up to 10,000 pounds (about 12,974 US dollars) for those who fail to self-isolate as requested as part of its efforts to urge Britons to follow the rules.
Besides, London Mayor Sadiq Khan warned that London should be placed under new lockdown restrictions as early as Monday to curb the recent surge in cases, local media reported.
Britain recorded another 3,899 infections overnight on Sunday, as the death toll rose by 18, according to official figures.
British Prime Minister Boris Johnson has warned that a second wave of COVID-19 in Britain is "coming in", and his government may need to "intensify things to help bring the rate of infections down."
Countries such as Britain, China, Russia and the United States are racing against time to develop coronavirus vaccines.
Hancock said he remained hopeful that a vaccine would be ready before the end of the year.
"We’ve got the cavalry coming over the next few months -- the vaccine, the mass testing and the improvements in treatments -- but we’ve got to all follow the rules between now and then to keep people safe," he said.
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