Some insurers will charge a premium. As with all things though, you need to shop around.

I buy a lot of Cat D cars to repair and sell on, which sell pretty easily if priced well and backed up with a CD full of pictures of the car pre-repair and the during the repair process.

Cat C's are generally harder to shift, and I usually steer clear of them to sell on unless the price is silly low or it's a specialist car. If you want one for a keeper though, Cat C's can represent a good buy.