If you can pay for the damage to the third party car then great, but, if someone was in the car, they may suddenly think 'personal injury' and have an ambulance chaser after you, at which point your insurance may decline to get involved as they state you should have told them instantly.

Make sure you dont leave it too long to decide and make sure you have covered your ass, and remember, just becuase you could get work done cheap, doesnt mean the third party will want to, they may want to use a large garage/bodyshop who may charge £££££££ more than you could get it done. Also you have to sweeten them a little as whilst their car is repaired, they may not have acess to a courtesy car unless the garage off one free of charge whilst they do the repair.

An bump with £800 damage is not an £800 claim, it is way way more.