This might seem obvious but why get his insurance company involved if the damage is only minor. He would be better off to pay for the damage direct especially if he is your neighbour.
Someone ran into the back of my car a few years ago and it was on private land.
I was lucky as he was waiting for me when I came back to the car.
He agreed to pay for the damage himself and arranged for the car to be repaired.

ROG/RS