a cat d repaired car can go back on the road without having to be inspected by DVLA,
However a cat c write off would have to have a VEHICLE IDENTITY CHECK done by a authorised DVLA garage. - it costs around 27-00 for the check.
DVLA usually will contact you to tell u that you wouyld need this done. Then you have to fill out a form send it to the nearest authorised garage and tehy will give an appointment date.