I'm in the very same position. Car crashed into me from behind a few weeks ago, didn't seem like much damage to the car at the time but the insurance have written it off. Cost of replacement car is cheaper than the repairs.
I hadn't realized how it worked and I thought if I pushed it I could make them repair the car as it was only body damage, no affect on the chassis or engine and its driving fine, just passed NCT, new tyres etc (before crash) and I didn't want the expense of getting a new car, but nope I can't do that. So I've just purchased a new car (well not new) to replace mine when I had no attention of upgrading my car this year.
Car's have dropped in value so much over the last year just makes it so much more annoying to be the innocent party and be left having to replace the car. I had mine valued with my insurance company for 9,000 I hadn't thought to change it and I wasn't advised to either.
My situtation was car was valued at 5,000. 6,514 damage. So at least I could get a car for the 5000 so not too bad. But just as another point, what I didn't know was the 3rd partys insurance company find a buyer for the car, highest offer they got was 650. So they give me the difference 4350 and I can sell for 650 to this person or try sell myself. In order to make up the 5000. Makes sense when I thought about it after, but I was confused about the whole thing when they rang me.