Wow, so much really useful advice being offered up by everybody, I'm overwhelmed by it all, give yourselves a huge pat on the back, especially @skomaz, @J.R. and @EnterName .
Over the years I have had a few accidents and have been with many different insurance companies and IIRC they have all operated similarly, i.e., sent a hire/loan car and then a transporter from the appointed body shop to collect the damaged vehicle and I cannot recall a single time when the assessor came to me to inspect the car. I assumed that was because to be certain that there was no structural damage that they would require to inspect beneath the vehicle, so needed either a pit or a lift to do so. In all but three of those accidents, I was driving company vehicles, so I never thought twice when the same approach was used on this occasion, after all the only thing that had altered was that I now owned the vehicle and the insurance policy was in my name.
In fact since I purchased the vehicle upon my retirement, I had my first accident in this car, again not my fault, a lorry pulled out from the slow lane to avoid a stationary car and sideswiped me, the second in this car was when I stopped at a roundabout to allow vehicles already on it to continue, another rammed me in the rear, (again not my fault). On both of those occasions I was asked to drive to the body shop, and then they gave me a courtesy car.
So as you can see, there was no reason for me to react in any other fashion, it just seemed to flow naturally along the same line as the other had done before. I have a different insurance company this time around, though. Perhaps the whole culture has changed for the worse now with all these accident chasers trying to get in on the action for a quick buck?
For instance, after the other driver and I changed details like, names, phone numbers and registration numbers etc and taken photos of both cars, we went on our way. Later that evening I got a text message from the AA about the accident saying that they would take care of the accident, pick up my car and get it repaired FOC. This I thought was the because the other person was insured by them. I never acted on the message straight away and in the morning I received an email from Tesco Bank who were claiming to be the insurers for the other party and after a quick phone call the other party confirmed that Tesco was the insurer and AA were they were with the AA for breakdown cover. So it was confusing at the start of it.
All of my accidents have been not my fault though and none as far as I can remember have resulted in either the loss of NCD or a hike in premiums, this one being the exception.