In England, Boris Johnson effectively cancelled Christmas for almost 18 million people in London, south-eastern and eastern England as the region was put into a new two-week lockdown from Sunday.
Under the new Tier 4 rules non-essential shops - as well as gyms, cinemas, casinos and hairdressers - have to stay shut and people are limited to meeting one other person from another household in an outdoor public space.
Those in Tier 4 were told they should not travel out of the region, while those outside were advised against visiting.
"What is really important is that people not only follow them (the new rules) but everybody in a Tier 4 area acts as if you have the virus to stop spreading it to other people," Mr Hancock told Sky News's Sophy Ridge On Sunday programme.
Scientists on the Government's New and Emerging Respiratory Virus Threats Advisory Group (Nervtag) have concluded the VUI 202012/01 mutant strain, identified by the Public Health England laboratories at Porton Down, is spreading more quickly.
The Prime Minister was advised of the group's conclusions at a meeting with ministers on the Covid O Committee on Friday evening, and the new regulations were signed off by Cabinet before Saturday's announcement scuppered many people's plans to see family for Christmas.
"We know with this new variant you can catch it more easily from a small amount of the virus being present," Mr Hancock said.