I started by phoning them up at 10pm on a Sunday, at which point they surprised me by answering the phone and kicking off the claim. The day after, they phoned me back in the morning to book me in at the body shop.
One day later, the body shop gave me a courtesy call to make sure I really wanted to wait as long as I'd said before I brought my car in, in case there'd been some kind of mistake in the booking (I was going to Kavey and Pete's in the meantime, and I wanted to do it in my car rather than a courtesy car. Long journeys need an iPod connector :) )
I took the car to the body shop on the appointed day, and they had a courtesy car waiting for me. A couple of days later, they called me to tell me mine was ready. I drove their car back that afternoon, signed the only two bits of paper that were involved in the entire process, from what I remember, and drove away in my shiny happy car.
A few days after that I got a text from the RAC asking me if everything was okay, and to give them a bell if it wasn't.
So. Like I said, I've just sent them a "thank you" card, and I don't think I'll be shopping around at the next renewal.