Ministers are also preparing to ban households from meeting indoors in an attempt to clamp down on cases spreading through social contact.
The proposal was described as a "total social lockdown" by The Times, which claimed the new restrictions could apply to London as well as large parts of northern England.
Schools, shops, factories and offices would stay open, however.
A government source told the paper that the restrictions were among the options considered last week before the Cabinet decided to introduce the 10pm curfew on bars, restaurants and other hospitality venues.
Watch: What are the new Covid-19 measures for pubs?
"The nation and the party wasn't ready for us to go any further last week," the source was quoted as saying.
"Unlike the first lockdown, nobody has seen pictures of body bags in Spain or France on the TV yet, which had a very powerful effect.
"Toughter measures on social interaction will have to come though. They're inevitable if you look at the numbers."
Earlier this week the UK reported a record number of new coronavirus cases, 6,784 in one day, as experts warned that hospitalisations and deaths were also starting to increase again.
More than a quarter of the UK population is already under local lockdown, with restrictions applying across large parts of the North West of England and Greater Manchester, the North East, West Yorkshire, West Midlands and Leicester, as well as Cardiff and Wales in Swansea and seven council areas in Scotland including Glasgow City. Neath Port Talbot, Torfaen and the Vale of Glamorgan will go into local lockdown from 6pm on Monday.
Watch: Steve Baker calls MPs to have greater say on Covid measures
Scotland has already introduced tougher restrictions which ban people from making indoor social visits to other households.
However Boris Johnson is facing a rebellion by Tory backbenchers who are urging the government to give MPs a chance to vote on coronavirus measures before they come into force.
MP Steve Baker warned that "liberty dies" with the government "exercising draconian powers" without parliamentary scrutiny.