Young drivers could be banned from carrying passengers for nine months after they pass their test.
Transport Secretary Patrick McLoughlin said he was considering the proposals, put forward by the Association of British Insurers (ABI).
The ABI said the move could cut the number of accidents involving young motorists.
Mr McLoughlin said: "I read regular reports where three or four young people have been killed in a car and it's a new driver and you wonder what happened.
"When I talk to young people who have recently passed their test, they say sometimes that there is peer pressure put on them to go fast, to show off.
"They are not drivers with a huge amount of experience by the very fact of them being new drivers. I think we have got to look at that."
Mr McLoughlin said he was considering whether measures should be put in place for novice drivers to carry no passengers other than immediate family members.
Ollie Pain, 18, and passenger Harry Smith, 17, died when their car crashed on a country lane through Furzeground Wood, only a few miles from North Nibley, on Tuesday night.
Teen Jake Gardner from Guiting Power was killed in a crash with another car on November 5. He was alone in the car, and there is no indication of what caused the crash.