If you cause damage to someone else's property, through your negligence, you are liable to meet any reasonable claim for repairing the damage. That applies to all situations (e.g. kicking a football through the glass of your neighbour's greenhouse). Motoring accidents are no different. It's still your duty to ensure that the damage is repaired. The fact that you have insurance (as required by law) doesn't change the position. You may claim on your insurance but, as long as you meet the claim, you will have discharged your obligation. (i.e. you're not forced to claim on your insurance).
However, it's a standard condition of all insurance policies that you're required to notify your insurers of any accident which you've been involved in (irrespective of who was at fault or whether a claim is made on anyone's insurance policy). So you should still contact your insurers.
Chris