Well, that was 1 of my cats trying to help me!! I shall start again!
It sounds like pica, which is when an animal has an odd craving for usually inedible things...and wool often crops up in the list.
This sort of behaviour is thought to be sometimes behavioural, and sometimes caused by dietary needs not being met by their food. Also it is more common in the exotic breeds, so your Billy being British Shorthair may have something to do with it.
There don't seem to be any drugs to cure it, but I have heard of extra fibre in the cats diet helping by keeping the cats guts busy. I suppose it'd only be a problem if he was ingesting large quantities & that would only happen if your carpet is particularly thick.
If it's an anxiety type thing, sort of grooming gone mad situation, then the solution would be to find some new toys perhaps & exciting games to divert his energy away from carpet cleaning!
Good luck, it might just be a 'Billy thing' that you have to live with!