Drivers who attend a speed awareness course instead of taking a fine and points on their licence may see their insurance premiums increase.
The BBC has learned that Admiral is treating it as if it were a conviction, even though the police do not.
The insurance group says its statistics show that drivers who have attended a course, pose a higher risk.
The Association of Chief Police Officers say Admiral's stance could harm efforts to improve road safety.
A spokesperson for Admiral told the BBC's 5 live Investigates programme: "Although a speed awareness course is a replacement for penalty points, it does not change the fact that the person involved has committed a speeding offence."
"Our claims statistics show that drivers who have committed a speeding offence could be a higher risk than drivers who do not commit speeding offences.
"This means that people attending a speed awareness course are more likely to make a claim and we price these risks accordingly," the company said.
The increase in Admiral's premiums comes despite assurances from some police forces and councils that attending a speed awareness course does not affect insurance policies.
Cumbria Constabulary's website says: "By attending the speed awareness course you... retain your current insurance premium."
The website of South Yorkshire Police says: "Attendance on a course would have no impact on the driver's insurance premium."
The BBC has also spoken to drivers who were told by their course instructor that attendance would prevent their premiums increasing.
According to several drivers, the promise that insurance premiums will not increase is a key factor in their deciding whether to attend a speed awareness course - even though they are often more expensive than the standard speeding fine of £60.
However, the programme has learned of a number of cases where drivers have seen their annual premiums go up by hundreds of pounds as a result of going on a course.
One driver in his 20s told the BBC his policy rose by £300 after informing insurance company Elephant - part of the Admiral group - he had been on a speed awareness course.
Another Elephant customer, Graham Taylor, from Oxfordshire, says his premiums rose by £80 after telling the insurer he had attended a course.
Paul Gemetta, from Hersham in Surrey, was caught speeding earlier this year and also opted to attend a course, rather than have points added to his licence.
"I thought it would be better to go on a speed awareness course, partly because I had not done any formal driver education for a long time," he told the BBC.
"It avoided me having any points and... on the course there was a very strong implication that insurance premiums wouldn't go up as a result of attending the course," Mr Gemetta said.
However, his renewal quote was £60 higher after completing the course - the same increase charged to Craig Wright, from Prestwich, another driver contacted by 5 live Investigates.
Admiral says it considers attending a speed awareness course as information relevant to pricing an accurate premium and told the BBC: "On the list of offences on our website, speed awareness courses are listed. The question is also asked on the phone at 'new business' stage and on our invitation to renew documents."
'Not a punishment'
Police say independent research shows speed awareness courses are very effective in making people think about the way they drive.
The Association of Chief Police Officers (Acpo) say the insurers' new policy could harm the purpose of the courses.
With no incentive to avoid increased insurance premiums, police fear drivers may opt to pay a fine instead and reject the courses.
Acpo's lead on roads policing, Deputy Chief Constable Suzette Davenport, told the BBC that going on a course is "not a punishment".
"We would argue that this is about improving road safety and therefore reducing risk, so it is a real concern to us," Ms Davenport added.
"I've had many letters come to me that say 'this was a really good course, I will do things differently' - if people are doing that then that is reducing the risk.
"I think therefore it is unfair that insurance companies are loading premiums. It's not appropriate."
Speed awareness courses are offered throughout England, Wales and Northern Ireland, but not in Scotland. In 2010, 447,724 people completed a speed awareness course and that increased to 772,430 in 2011.
An independent survey, commissioned by Acpo, of more than 2,000 people who had taken a speed awareness course, found that 99% of drivers claimed to have changed their behaviour as a result of attending.