Funnily enough, Ive had 2 non-blame claims in the last few years, once when my LJ78 was totalled, and once when the missus D4 got damaged in a car park.
On both occasions Ive used the other parties claim service (so not my own insurance). At the start of the conversation Ive explained that I know its cheaper for them that way so expect the matter to be dealt with quickly and realistically on their part. For the LJ I did really well, and the missus D4 got repaired by Land Rover whereas my own insurance wanted to use their own repair centre.
With my current ongoing claim (against me) AF simply passed me on to my insurance company.
Knowing how the system works is advantageous.
Im happy with AF, other than looong phone wait on an 0845 number, but.......as with all such numbers, look for the Overseas Caller number, it will be a UK landline!
Pete