Criminal checks on driving instructors should be made compulsory, according to the Driving Standards Agency.
The Driving Instructors Association is backing the checks
The DSA - the driving test organiser - is proposing that all driving instructors should be checked using Criminal Records Bureau data.
The checks would be aimed at safeguarding the public from harm.
Eddie Barnaville, chief executive of the Driving Instructors Association, said such checks were "vital to protect young people learning to drive".
He added: "The CRB checks are vital to ensure the instructor is fit and proper and able to teach every individual to drive.
"Many parents put their trust in instructors to teach their children how to drive, and believe they are in a safe environment.
"Teachers in schools and playgroups are required to have such checks. I would like to see these checks incorporated as soon as possible so we can protect teenagers and young adults learning to drive."
Provisional driving instructors and approved driving instructors are required to declare any motoring or non-motoring convictions, and court proceedings that may be pending, while registered or seeking registration.
They also have to provide the details of two referees.
However, their criminal history is not always thoroughly checked through the CRB.