Very good question, and one with two responses. Under the road traffic act 1934, you only need to notify your insurer when you have been involved in an incident that might cause someone to raise a claim against you. That is the first response,
The second is that insurer and price comparison sites have "bastardised" it to to mean have you ever been involved in "any" incident. Under the 2015 insurance act, any questions asked by an insurer have to be relevant to the risk they are insuring. I cannot see how being hit by another driver while out with your instructor on a lesson, should penalise your future insurance premiums. I believe the very same thing for any non fault incident, as they will penalise you even though it is and was no fault of your own.

My personal response to the above is no. You do not need to make your current insurer aware, as the contract of insurance your ADI has is different from a normal consumer policy. The response I have to give on Honest Johns behalf is that if you are unsure, you must always speak to your insurer and ask them that question.The best thing to do, is have you ADI ask his insurer that question, have the response documented.