Exactly what i done and just as well i did as just after the assessor came and put it down to the same as yours (beyond economical repair ) a recovery truck turned up to take it away before any setalment had beed offered or agreed on.
I contacted My Insurance and then we agreed on a value and for me to keep the "salvage" which was valued at 10% of the agreed value.
I got to keep the car and got a cheque through the post in a couple of weeks.
The normal option is for the Insurance to take it away )normaly as far away for you as poss) and once you decide you want to keep it you will have to pay the storage from that day on plus any recovery costs and you also have the risk of some of the parts going missing while its in the pound
So, get it in the air
Regards
Ian