Under the current rules, people can form support support networks in a so-called bubble with another household in specific circumstances.
There had been speculation the policy could be scrapped amid calls for lockdown restrictions to be tightened. Earlier on Monday, Boris Johnson suggested the lockdown could be made stricter if people do not follow the current rules.
But Hancock told a Downing Street press conference that bubbles would not be scrapped.
He said: “I can rule out removing the bubbles that we have in place. The childcare bubbles, the support bubbles, are very important and we are going to keep them.
“I know how important they are to people and they are an important part of the system we’ve got to support people whilst also having these tough measures that are necessary.
“The bubbles are there for individual specific people – so, for instance, if you bubble with somebody, that is the person you have bubbled with. You can’t keep moving bubbles. It’s very important.
“So somebody in your bubble essentially becomes effectively part of your household.
“So it is important people stick to the same bubble, but the bubbles policy will stay.”
People who live alone, sole carers, parents of babies under one, parents with disabled children under five who require continuous care, 16-or 17-year-olds living with others of the same age, and single parents can all form support bubbles with one other household.
People with children under 14 can form a childcare bubble, to allow friends or family from one other household to provide informal childcare.
The government’s scientific advisory group for emergencies (Sage) had in fact warned ministers away from using the word “bubbles” in early December, saying: “Consideration should be given to ensuring that current social bubbles policy reflects the needs of minority ethnic groups living in larger multigenerational households; and also communicated in a meaningful way so that it is clear how it applies to their households.
"For example, the term ‘bubbles’ does not translate easily into non-English languages so alternative terms should be identified which will resonate.”
Earlier, Johnson warned that coronavirus rules could be tightened if the lockdown is not “properly observed” by the public.
The prime minister said the regulations would be kept “under constant review” after England’s chief medical officer said the NHS was entering its “worst weeks of the pandemic”.
Professor Chris Whitty said the UK had a “serious problem” with infection rates with the number of instances of the new variant “rising in every part of England”.
On a visit to a vaccination centre in Bristol on Monday, Johnson said if the current rules were followed they could make a “huge difference” in suppressing the virus.
But he added: “We’re going to keep the rules under constant review. Where we have to tighten them, we will.”