Batman's King Of Cats is Catwoman's brother. That's literally his whole deal.
Batman initially mistook them for lovers because Catwoman wouldn't help him track the King Of Cats down. Nice detective work.
Tom Baker is the Comics Editor at WhatCulture! He's heard all the Doctor Who jokes, but not many about Randall and Hopkirk. He also blogs at http://communibearsilostate.wordpress.com/