It's all dependant on the ins company but let them know your interested and you'll get an answer back then.
A lot are auctioning them via copart etc now as stated above cos their aware of the value of them,a lot have teams now to deal with it.
If there's any dispute regarding fault be careful with paying the recovery firm direct,you may really struggle to get your money back,ins companies are total cunts to deal with and I've had horrendous run ins with them myself so don't be surprised to see a £5-600 bill need settling from the recovery firm first.