It is disgusting that your insurance company can remotely write off your car as a CAT S without inspecting it. My understanding of CAT S is that there is structural damage to a car but insurance companies are a law unto themselves. How old is your car and what value as this may be what is guiding their decision. If it is only a dented door it is a pity that you advised them in the first place, but you cannot go back. On the legal side you have to go with what the insurance company say so it is back to them but a would seriously challenge it. They are writing off CAT S cars everyday so they do know what is involved

A CAT S is marked on the log book after an inspection for roadworthiness. It should not be any more difficult to insure but its retail value will be very much less than a good one

yes you are correct no inspection is legally required which is a considerable loophole in the whole insurance damage saga. when you see the pictures of some cat S cars you wonder why anyone would buy one.

The insurance company have a legal obligation to notify the DVLA. It is probably too late to challenge them on the classification, From what you describe it should have been a CAT N and you would not have this hassle. I should keep your pictures should you want to sell it in the future.