You are legally obligated to tell your insurance firm you have had an accident, even if you have admitted some guilt, which you should not have done, nothing is to say that the other party won't turn nasty and claim for whip lash, especially if witness present?
Your insurance firm will advise you what to do,even if you tell them you don't wish to make a claim.
Normally any accident should be reported to the Police within 24 hrs, if you opt out and it backfires your in deep water, don't risk it if you have nothing to loose?
I was recently hit up the rear (only slight damage to the rear bumper). I have to hold my hand up and say it was partially my fault. That being the case I agreed with the other driver I would pay the very slight damage sustained to the front of his car rather than go the insurance route. However, as his motor was a bit of an old banger, who can I contact to find out if his car has an up to date and valid MOT?