Taking a speed awareness course could lead to increased insurance premiums.
Admiral is raising premiums of people who attend the courses, which are offered instead of a fine and licence penalty points.
The insurance group says people who attend the course pose a higher risk.
Avoiding extra insurance costs has been a key attraction of the courses, which are typically more expensive than the £60 fixed penalty fine for speeding.
Some police forces have marketed the courses with claims that insurance will not be affected.
An Admiral spokesman told the BBC: “People attending a speed awareness course are more likely to make a claim and we price these risks accordingly.”
ACPO’s lead on roads policing, Deputy Chief Constable Suzette Davenport, said: “It is unfair that insurance companies are loading premiums. It's not appropriate."