Maximum fines for speeding on motorways could increase from £2,500 to £10,000.
The move is part of proposals to increase the maximum fines that can be imposed by magistrates across England and Wales.
Fines for other speeding and driving without insurance offences could also see increases.
Justice Minister Jeremy Wright said: "Magistrates are the cornerstone of our justice system and these changes will provide them with greater powers to deal with the day-to-day offences that impact their local communities."
RAC Foundation director Professor Stephen Glaister questioned the proposals.
He told the BBC: "People who break the law should bear the consequences but this seems such a wholesale change to the system so you have to ask what was going so badly wrong before.
"Ironically we know that speeding offences have declined over recent years and just last week the Department for Transport confirmed that, even after taking congestion out of the equation, recorded traffic speeds have been dropping for a decade on all types of roads."