It all depends on the category of the write off.(actually more correctly defined as "beyond economical repair") I "googled" this and got the following:
Category A requires total destruction of the vehicle and even good usable parts cannot be stripped from category A losses, and legally sold. The licence for the registration mark is retained by the DVLA.
Category B is less severe in that it can only be used as a donor for parts and cannot be repaired for use on the road. The mark is retained.
Category C is a damaged vehicle with the potential to be repaired and put back on the road, that is beyong economic repair using brand new parts. I bought a Cat C write off, and repaired it, so I have first-hand experience. The repaired vehicle has to undergo a special test at one of a select number of SVA test centres, not the run of the mill testing stations, which it must pass in order to obtain a certificate of authorisation to apply for a registration mark. Once overcoming that hurdle the vehice then has to pass the standard D.O.T. test or MOT as we call it. As the registration mark, or again more correctly, the right to use the mark on a vehicle( we never own a registration mark) is retained by the DVLA, upon application for a registration mark, it could be possible that you get the mark with which the vehicle was issued upon its first registration in the U.K., an age related plate, or the last previous non-private style plate. In my case the vehivle was on a private plate which the previous owner managed to retain but the mark it now caries is non-transferrable
Cat D is a damaged vehicle that the insurance company decide not to repair
CAT F is fire damaged, much the same as CAT D
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