A note of caution. I had an accident about 4 years ago when I had my TTS - someone ran in the back of me. They didn't do a runner and they were happy to pay for the repairs. I phoned my Dealership to arrange an inspection, and they offered to put my on to their 'accident management service'. This wasn't to my knowledge 'Ensurance' but it looks similar.
The accident management company arranged for repairs and a replacement TT (2.0T Coupe) whilst mine was in for repairs.
As it happens, I mentioned this to a friend who was also an Audi driver and he told me that he had had a bad experience with the accident management company in similar circumstances. Basically, they make money on the car hire and so it is in their interest for the process to take a long time. In my friend's case it took 10 days and the other party ended up contesting this, and he had some tense time when they were going to come after him personally for the costs on the hire.
Because of this, I was hot on the accident management company and they outright lied to me about the progress on my car (saying the body shop was shut on a day when I had personally called them directly). I rode them and the job was done with just 3 days hire needed. The repair was a new bumper with reversing sensors.
The accident management company butt f**ked the poor guy who ran in the back of me. When they took him to court and I saw the claim it was for £4500. For three days hire and a new bumper!
So, I now approach accident management companies with extreme caution - it's the new 'whip lash' as far as I can see. And we all end up paying in the end...