The Conservatives are calling for the speed limit on motorways to be raised to 80mph.
The laws on speeding generate rage in the tabloids
Shadow transport secretary Damian Green is tabling an amendment to the government's Traffic Management Bill.
He believes it is the best way to give motorists more freedom without affecting safety.
The Department of Transport said the idea had previously been rejected on road safety grounds but would be kept under review.
The speeding laws and their enforcement has become a major political issue, helped by tabloid newspapers.
Many feel motorists are being unfairly targeted over speeding to raise money, when drink drivers and those who are disqualified or without insurance cause many accidents.
There was an outcry recently when a levy on speeding fines to go towards victims of crime was suggested.
Mr Green said: "This is part of a wider campaign we have got for more realistic and appropriate speed limits.
"While we are arguing that the speed limit on the motorway should go up from 70 to 80mph, we also argue that in other areas, for instance near schools, parks and hospitals, the speed limit should be reduced to 20mph.
"We should be more sensible and more variable in the speed limits we have to reflect the dangers both to drivers and, equally importantly, to pedestrians, particularly to children."
The backbench Labour MP John Mann will put forward a similar amendment. He wants the maximum speed limit on motorways to be 80mph in good weather, but 60mph in bad weather.
He said: "For too long we've had over-simplistic speed limits.
"Having a variance that increases the speed to what most people seem to do on the motorway, to 80mph, and also to enforce it then at 80mph, but also to reduce it in bad weather to 60mph...would be something that most motorists would approve of."
Of the two major motoring organisations, John Dawson, director of the AA Motoring Trust, said most drivers did not want the speed limit to be raised - only for everyone to drive 10mph faster.
"Motorists don't want the driven speeds on motorways to change and there's no
safety reason to change it - motorways are incredibly safe," he said.
"If it were raised, it would have to be enforced at 80mph."
Edmund King, executive director of the RAC Foundation, argued that speed limits should be reviewed.
He said: "There should be a review of speed limits, and 80mph in a modern car,
on a good road surface at a safe distance from the car in front, is perfectly
He said Britain needed "a more intelligent approach to speed", with better
policing of bad driving and more flexible speed limits.
"On a motorway, 50mph is too fast if you're driving too close to the car in
front," he said.