There are fears the Government is expected to award two points to drivers travelling at one or two miles per hour over the limit.
The penalty could increase to four points if drivers go 5mph to 30mph over and six for those exceeding the limit by more than 30mph.
But such a move will not curb speeding, says the Royal Society for the Prevention of Accidents (RoSPA).
Kevin Clinton, RoSPA's head of road safety said: 'People must be discouraged from speeding. We are concerned that lowering the number of points for people just over the limit might weaken the deterrent effect of speed enforcement.
'We do not want anything introduced that implies that exceeding the speed limit, even by a small amount, is a minor offence, because it is not. At 35mph a motorist is twice as likely to kill a pedestrian as at 30mph.'
Transport Secretary Alistair Darling said: 'We must reduce speeding but the public must have confidence that the punishment fits the crime.'
Brian Gregory, chairman at the Association of British Drivers, has also criticised the move.
He said: 'This latest fiasco reminds us how urgently the Government needs to sack the social engineers who are creating these daft ideas and replace them with road safety experts, perhaps from a traffic policing background.
'Then perhaps we could begin to get a speed enforcement regime that would be focused on safety and bear relation to danger caused by the offender rather than being based on irrelevant numerical values.'
The RAC is urging the Government to take into consideration the circumstances of the offence before issuing points.
An RAC spokeswoman said: 'Who is to say that travelling 10mph above the speed limit on a dual carriageway late at night is a more serious and dangerous offence than going 5mph above the speed limit outside a school?'