I was in a similar position a while ago.
My friend crashed my car (he was a named driver on my policy) with no other cars involved. It was a good few years old, but I'd looked after it, so it was in good condition for its age (I can't remember but I reckon it was approx 10 years old).
Anyway, they took the car, assessed it and said it was not economical to repair it. I asked if I could have the car back so I could get a local garage to assess it and possibly repair it. They asked the engineer and because it was still structurally sound, they let me buy it back. They paid me the market value of the car minus £200 (that was the value put on the car in the condition it was in).
Well, I got the car repaired and I had to inform my insurance company, so that someone could come out and assess it, to make sure it was road worthy etc.
The thing is, the garage quoting for your repairs will prob be quoting top whack prices, with new parts from the car dealers, whereas my friend who has is own garage gets his parts from local motor factors at a fraction of the price.
So in answer to your question, you do have the option to take the car back and take it to your own garage - wait and see if they tell you if it's a write off, then ask them what category write off it is ... then refer to:
http://www.rac.co.uk/community/blog/rac-blog/september-2011/what-is-an-insurance-write-off/