Keithp, give them a warning. tell them that they have two weeks to show you proof / receipt of vetinary care or out of concern you will need to inform an animal protection organization so that they can monitor the situation.
If the relative refuses - you gave them fair warning. call your local RSPCA. I think, they don't always take the animal off the owner, most of the time, they will try to enforce care and give the owner a chance since some owners are dumb creatures, and they monitor it - like social services for children, depending on severity.
Ie, in your case, they'd probably give an ultimatum, get vetinary care or we will take your animal. Then they'd come back in a few days and if the situation isnt resolved with proof, then they'll take control.
If the cat is loosing weight and looks poorly, you need to step in to some degree before its too late. Give the owner a chance, then take matters into your own hands - after all you did warn them.