Cat D doesnt need and inspection after repair but stays on for life. Cat c write off would need inspection to make sure identitiy of car as alot of people were nicking a car then swaping the chassis nos and its a check just to make sure thats that hasnt happened and to cut down on car crime but still stays on. If they checked to find this and couldnt identify the year of the shell if say you shell changed it then could go on a q. Cat d means really that repairable but insurance decided not to repair cat c normally means stuctural damage but beyond economical repair but can go back on the road. Cat a/b cannott go back on the road and will only sell to a breaker. It has an impact on insurance as if you buy a cat c then write it off they would pay less out so be carefull. Cat c cars normally re sell for alot less as cat d people dont see to be so fussed about.

Hope this helps all this information is on the dvla website. and quite helpfull.

Cheers