Drivers caught breaking the speed limit by more than 20mph could face a six-point penalty under new proposals.
The government's consultation paper on road safety also says motorists found speeding in such a way twice could be automatically banned from driving.
The document also suggests creating formal drug-drive limits in a bid to make prosecutions easier to achieve.
However, ministers say any changes in the drink-drive limit would need solid evidence of the safety benefits.
Road Safety Minister Jim Fitzpatrick told the BBC's Today programme the measures were about "being on the side of the safe motorist".
The government wanted to address the 2,946 deaths and the 30,000 serious injuries on British roads last year, he said.
Family's anger at drink drive laws
"Notwithstanding that these are the best figures we've ever had, we know that we can do more and that we can reduce the numbers of people being killed and seriously injured and that means looking at speeding, drink driving, drug driving, careless driving and people not wearing seatbelts."
Ministers would also be looking at whether the drink-drive limit was at the right level, he added.
The road safety charity Brake welcomed the planned increase in the fixed penalty system but warned changes could cause confusion.
It said it would oppose plans to cut the number of points for people caught speeding at only a few miles over the limit.
It also said it wanted tougher charges, not just fines - particularly for drivers speeding through towns, villages and on bendy rural roads.
As the law currently stands, the majority of speeding offences are punished with a fixed penalty notice of a fine and three points.
But the government wants to introduce more severe punishments for so-called "excessive speeders" - for example, those who drive at more than 90mph on a motorway.
If adopted, the proposal - first mooted four years ago - would see these "anti-social drivers" who drive more than 20mph over the limit automatically given six points.
Being caught twice at such speeds would mean 12 points and an automatic disqualification from driving.
The president of the AA, Edmund King, told the BBC his members were concerned whether the proposals would be accompanied by adequate warnings about changes in speed limits.
"They feel that there are many areas in the country where you change, say from a 70 limit to a 50 limit, or a 60 to a 30 limit, and it's not well signed and there's not much of a distance between the change of limits.
"So obviously what we wouldn't want is someone losing their licence because a speed limit was obscured by a tree, or the sign wasn't very clear."
The government also wants to crack down on drivers who use drugs, particularly the "hard core of frequent drug drivers who are primarily males aged between 25 and 35".
It estimates that up to one in five motorists killed in road accidents may have drugs in their system.
It is vital that the public is educated about the dangers of drug-driving and that the police are given more support
Dr Vivienne Nathanson British Medical Association
There are currently no drugs breathalysers and no legal "driving limit" for cannabis, heroin or cocaine, so the onus is on officers to prove that someone is impaired.
Ministers are considering whether introducing formal drug limits could make it easier gain prosecutions.
Dr Vivienne Nathanson, of the British Medical Association, welcomed the move.
"It is vital that the public is educated about the dangers of drug-driving and that the police are given more support, both in training and resources, so that they can tackle this dangerous issue."
But she said the body would continue to lobby the government to reduce the drink-drive limit.
Shadow transport secretary Theresa Villiers said ministers needed to realise that if they wanted to get tough on the most anti-social drivers, they would not catch them with speed cameras.
"If there are no traffic police to pull people over and breathalyse them, the government's proposed crackdown will be nothing more than yet another empty headline."
The number of people killed on British roads last year fell to the lowest level since records began, transport department figures show.
Just over 2,940 people died in 2007, a drop of 7% from 2006, with child deaths dropping 28% to a record low of 121.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.