Ok just to clear a few things up because this to and fro is getting boring.
Yes many insurers include a clause in their terms and conditions stating that you must inform them if you have an accident even if you are not claiming. I guess they do this because insurers work on risk and by being involved in an accident, even if you are not claiming, to them you become a high risk and therefore many will load your next year's premium as a result.
The reality is that 90% of people will not tell their insurer at all as that is the point of going privately.
What you do is up to you.