If you have banked a 'settlement' then the vehicle is the property of the insurance Co and thiers to dispose of however they think most eccomomical.
They may give you first refusal on it, they might not even bother telling you what they will do with it.
If you dont have a settlement, then basically the car is yours still, and you can argue the settlement to suit yourself.
I wen through it three effing times with a motorbike back in the early 90's; and wouldn't let them write it off on the first two (Outstanding HP was more than pay-out & I wasn't happy about 'scrapping' a brand new effing bike for the sake of a chisseled out lock and a few bits of cracked plastic!)
Something worth investigating though, is the new insurance write off schemes; used to be that for 'write off' to be recorded you had to send the V7 back to DVLA, these days I think that a 'Catagory Loss' can be writtedn against the reg no and chassis number, by an insurance company. Some catagories ie 'total loss' as deemed beyond ecconomical repair mean tha the car has to be SVA's for re-registration, as in the DVLA's eyes its been deemed far too damaged to be 'safe'.
If you WANT the car back, best to try and get it in your hands and assess the paint job for yourself, its a Landy for gawds sake, you can get a good enough cover of colour with a radiator roller!
See how bad it is, with the paint and any other dings and damage, and then argue with the Ins co for a cash settlemet on the repairs.
They are a lot more penny pinching these days, so if you are prepared to take a lesser payout, you may get a deal thats worth while, but tread careful they dont still write the car off at DVLA and find you get a 'tug' and told you are driving an unregistered vehicle or something1