I'm fairly sure they aren't marked on the log book. This only shows the current ownership of the vehicle. Theoretically the MOT is all you need to pass to get it back on the road, the Cat C check, I think is to verify the identity, primarly to stop ringing. The trick is to throughly inspect the car, as theowletman has said, nothing worse than doing a simple rear bumper change only to find that the impact has creased the boot and pushed the shell back, jaming the rear doors, so it would need an expensive shell pull to get straight. Occasionally you see a car gong down the road sideways, you know what has happen there. A friend reversed with his door open, and hit something; this distorted the shell so badly the car was Cat B. I check the door gaps; they should be constant all the way round. If they close up then something is not right, and walk away!.
Ken