The motoring group’s survey of 19,000 members suggested nearly a quarter did not know it was illegal to use a mobile phone while out with a learner driver.
Nearly one in 10 respondents was unaware falling asleep was not allowed.
The law states that somebody supervising a learner driver is effectively in control of the car.
In one case a supervisor was jailed after the learner was involved in a crash that killed two people.
It said many learners benefited from time spent with more experienced drivers, but suggested short driving courses for supervisors might be needed.
The AA/Populus survey suggested drivers were also breaking the law by drinking, sending text messages, or failing to wear their glasses while on practice runs with learners.
Some 23% of respondents did not know they would be breaking the law by using a mobile phone while supervising a learner.
And 13% were unaware of the need to wear glasses if they used them when driving themselves, while 9% did not realise that falling asleep in the passenger seat was illegal.
A total of 4% of respondents who had supervised learners admitted breaking at least one of these laws. The figure rose to 22% among supervisors aged 21 to 24.
The president of the AA, Edmund King, said the issue was highlighted by a case in which a person who was supposed to be supervising was over the drink-drive limit.
“This is where the legal point is quite serious because you are actually deemed to be in control of the car, even when you’re supervising. And in fact there has been a case where tragically the learner driver actually had a crash, two people died and the supervisor was actually deemed responsible and actually went to jail.”
Learners who build on skills they gain in formal lessons by practising with family or friends have a better chance of passing their test and are likely to be safer behind the wheel.
“Yet drivers often lack confidence or don’t know their responsibilities when supervising learners.
“Many are passing on bad driving habits or even risking a run-in with the law.”
Road safety charity Brake said it wanted to see the minimum age for accompanying drivers raised to at least 25.
Katie Shephard from the charity said: “It is vital that learner drivers gain suitable supervised experience behind the wheel, to ensure their safety and the safety of other road users. Accompanying drivers should also be registered as ‘approved accompanying drivers’ by completing a questionnaire to prove their suitability, which could be checked by their insurer.”
Duncan Vernon, road safety manager for the Royal Society for the Prevention of Accidents, said there was “no doubt” those who supervised learner drivers would benefit from being given more information about how best to teach.
“All-round good practice should involve better co-ordination with approved driving instructors, as well-planned private practice can be invaluable,” he said.
“It gives the novice more experience in all kinds of conditions, thereby reducing the risk of them being involved in a crash once they have passed their test.”
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