I have worked as a commercial insurance underwriter for the past 7 years and the stance we took for Cat D vehicles was this: The vehicle must have an engineer's report to state it has been repaired correctly (there is a name/code/abbreviation for this but after a beer I can't remember what it is...
) and a copy of a current MOT test (taken
after the damage has been repaired). Once this was all received the underwriters would generally be fine for it to be added to the policy.
However, in the event of any claim, the company would only pay out a MAXIMUM of 75% of the market value because the vehicle was Cat D. These criteria will doubtless vary from company to company but the basics will probably be the same