Currently, drivers in England, Scotland and Wales who do not buckle up are given a £100 fine.
The Department for Transport has not said how many points may be given.
Drivers can lose their licence if they build up 12 or more points within three years.
The law is different in Northern Ireland, where failure to wear a seat belt can lead to a £500 fine and three penalty points.
The new punishment for not wearing a seat belt is one of 74 measures included in the government’s Road Safety Action Plan.
The government is also considering fitting alcohol sensors to cars driven by people convicted of drinking and driving which will immobilise the vehicle if they are over the legal limit.
Transport Secretary Chris Grayling said the Road Safety Action Plan was a “key milestone” that sets out how Britain would try to reduce the number of people killed and seriously injured on its roads.
Steve Gooding, director of motoring research at the RAC Foundation, said: “It is barely conceivable that tens of thousands of drivers and passengers make the decision each day not to belt up.
“The direct effect of non-compliance might be felt by the vehicle occupant themselves in the event of a crash, but ultimately the emergency services are left to deal with the roadside consequences and the taxpayer foots the bills,” he added.
Seat belts and the law
- Use of a seat belt by drivers and front seat passengers in cars was made compulsory in the UK in January 1983
- Rear seat belt use was made compulsory for children in 1989 and adults in 1991
- Drivers and passengers caught without wearing a seat belt could be hit with an on-the-spot Fixed Penalty Notice of £100, rising to a fine of £500 if the case goes to court
- The driver is responsible for ensuring each child passenger aged up to age 14 wears a seat belt and could be fined for each child without a seat belt