you will not need to ask to buy it back its non fault, the best method is to deal direct with the other onsurance, it produces a much quicker turn around and also you wont need to pay an excess if they do repair

i use this method if an when need be, i had a car wrote off last year, i had a cheque in the post 9 days later, if i had left it to my co would of taken a couple months

they have no right to your salvage, keep the car at home, normally what will happen is eventually one of the reps from there insurance will call you. once the assessor has seen it you will have a call within a week, i however called them 2 days later, keep ontop of them, get there ref number once you have been in contact with them, tell your insurance company you want to deal direct with the insurnance co yourself as you feel it will be quicker.