Under the planned reforms, maximum fines for speeding on dual carriageways and for using a mobile phone while driving will also quadruple, going from £1,000 to £4,000. Driving without insurance could also see increases.
Any new legislation would first have to be debated in Parliament but there is no current timetable for any such discussion.
The planned punishments were immediately condemned as "disproportionate and draconian" by Rupert Lipton, the director of the National Motorists Action Group.
He claimed that fear of being hit with the maximum fine would stop innocent drivers from challenging unfair speeding tickets.
"If you wish to challenge you can currently face six points and a £1,000 fine on non-motorway roads or £2,500 on the motorway. Raising it four-fold is clearly an over-reaction.
"The threat and the fear of a disproportionate fine would deter many from trying to seek justice."
Mr Lipton was backed by Edmund King, the president of the Automobile Association, who said: "We would not condone excessive speeding in any way, but fines have to be proportionate. One has to question whether increasing the fines four-fold is proportionate. It probably is not.
"If we had more cops in cars on the motorway that would be a much more effective deterrent."
RAC Foundation director Professor Stephen Glaister also questioned the proposals.Mr Glaister said: "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."
The Ministry of Justice said custody would "continue to be used for serious offenders and fines will not become an alternative for those who would otherwise be sent to custody".
But Jeremy Wright, the justice minister, said: "Financial penalties can be an effective way of punishing criminals and deterring them from further offending.
"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."
. The Level 1 fine maximum increase from £200 to £800. Offences which may be dealt with by a Level 1 fine include unauthorised cycle racing on public ways
. Level 2 increases from £500 to £2,000. Offences include driving a motor cycle without a protective helmet
. Level 3 increases from £1,000 to £4,000. Offences include the sale of alcohol to a drunk person or being drunk and disorderly in a public place
. Level 4 increases from £2,500 to £10,000. Offences include speeding on the motorway
Magistrate fines collected at the end of 2012/13 reached a record high of £284m and continued to rise during the last financial year, the Ministry of Justice added.
