A new legal limit will ban larger groups meeting anywhere socially indoors or outdoors, No 10 said.
But it will not apply to schools, workplaces or Covid-secure weddings, funerals and organised team sports.
It will be enforced through a £100 fine if people fail to comply with police, doubling up to a maximum of £3,200.
Several exemptions apply to the new rules – which come into force on 14 September – with households and support bubbles bigger than six people unaffected.
A full list of exemptions will be published by the government later.
Prime Minister Boris Johnson is expected to deliver further details at a Downing Street news conference on Wednesday.
In a preview of his address, the PM said: “We need to act now to stop the virus spreading. So we are simplifying and strengthening the rules on social contact – making them easier to understand and for the police to enforce.
“It is absolutely critical that people now abide by these rules and remember the basics – washing your hands, covering your face, keeping space from others, and getting a test if you have symptoms.”
No 10 said any group of seven or more people gathering anywhere “risks being dispersed by police or fined for non-compliance”.
The change applies to people in England of all ages, and to gatherings indoors and outdoors, in private homes, public outdoor spaces, and venues such as pubs and restaurants.
BBC political correspondent Nick Eardley pointed out that pubs and restaurants would be allowed to have more than six customers inside, but that the groups of six would have to be socially distant from each other.
The rationale behind allowing this, but not allowing larger groups of people inside other people’s homes, is that businesses can only be open if they follow safety and hygiene measures set out by the government, he added.
The devolved administrations in Scotland, Wales and Northern Ireland are able to set their own coronavirus restrictions and, while largely implementing similar rules, have moved at their own pace during the pandemic.