"Every time you try to flex the rules that could be fatal" and staying at home was the "most important thing we can do collectively as a society", Hancock told the BBC.
Hancock did not rule out strengthening restrictions amid calls from scientists that the current rules need to be stricter, admitting that the National Health Service (NHS) was under "very serious pressure".
"People need to not just follow the letter of the rules but follow the spirit as well and play their part," he said.
Britain has reported more than 80,000 coronavirus-related deaths after another 1,035 were recorded, according to official figures released Saturday.
The total number of deaths within 28 days of a positive COVID-19 test stood at 80,868 on Saturday.
Meanwhile, Britain recorded another 59,937 coronavirus cases, bringing the total number of coronavirus cases in the country to 3,017,409, the data showed.
The latest figures were revealed as scientists advising the British government warned that the current lockdown measures in England need to be "stricter" to achieve the same impact as the shutdown in March 2020.
Robert West, who sits in the Scientific Pandemic Influenza Group on Behaviours, which advises the British government's Scientific Advisory Group for Emergencies (SAGE), said Saturday that the current rules were "still allowing a lot of activity which is spreading the virus".
West said due to the new variant of coronavirus, which is said to be up to 70 percent more infectious, the lockdown measures need to be tougher.
England is currently under the third national lockdown since the pandemic began in the country. To bring life back to normal, countries such as Britain, China, Germany, Russia and the United States have been racing against time to develop coronavirus vaccines.