The comments came from Chief constable Anthony Bangham, the National Police Chiefs Council lead on road policing, in a speech at the Police Federation Roads Policing Conference this week. He called for an end to the so-called "10% buffer" - and added that drivers should not "whinge" to police if they are caught over the speed limit.
More than a thousand of you had your say in our online poll, with a staggering 96% of voters saying that motorists should not be fined for breaking the limit by 1mph.
Since the speech, which took place on Tuesday, other police forces have joined in with criticism of the speech, with Chief Inspector Ian Hanson, chairman of the Greater Manchester Police Federation, branding Mr Bangham "out of touch".
Road safety campaigners supported the proposals.
Here's how you reacted to the story on social media.
Joe Tivnen: "Instead of 'whinging' about being 1 mph over the speed limit, why not concentrate on doing proper police work, like looking for terrorists, protecting kids from predators or looking for murderers?"
Allan Mcmanus: "You would have to be watching the speedo more than watching the road ahead if you are going to be certain not to creep over by 1mph, these people don't live in the real world idiots."
John Coxon: "The courts would overload with appeals and such ... impossible to manage and impossible to sustain ... unreasonable suggestion that would cause more accidents due to speedometer watching."
Martin Rodgerson: "Impossible, unless the car manufacturers come up with a 100% accurate speedo, which if they do will need calibration every week."
Les Shaw: "Speeding is not the major cause of road collisions. Bad driving is and he knows it."
Rob Irving: "I would never condone speeding but common sense tells you there has to be some margin for mechanical/technical error surely."
Duncan Mitchell: "My car has a speed limiter, which is not distracted by looking out of the window or thinking. Even this gives a range up to 2 or 3 mph above its set speed. If even technology can't achieve total obedience, us humans have no chance."
Gil Gamesh: "What difference does 1mph make?! They need to concentrate on issues like mobile phone usage whilst driving, or even burglary and violent crime."
Lisa Ball: "Not all cars have cruise control and slipping under or over (small amount) the limit is far too easily done unintentionally.
"Correction to follow immediately still takes a little time while being super observant of the road and surroundings. 1mph margin is too small. We’re only humans not machines."
Paul Fletch: "Speeding fines were always given out for anything over a 10% discretion - 30mph (33) 50mph (55) etc.
"This hasn't altered for years even with major improvements in breaking systems, improved tyre technology etc - so I would like to think we have it about right. There has to be limits based on the road layout, conditions etc as speed is a killer."
Eileen Jackson: "No, one over is not the same as 10 over!"
Tim Brown: "The current system of 10% leeway seems to work. Why change it?"
Andy Pounder: "I think they should just get rid of speed awareness courses - actually punish the real speeders financially instead of giving them the option to get away with the offence without a ‘real’ punishment!"
Chris Mason: "I think.all of us have drifted over the limit at one time or another. This is nothing to do with road safety it's all about raising revenue and the motorist is the easiest target."