Jack Russell Terrier. Or a slightly larger dog, but it does need to be compact and quick. My former lodger's "Bull Jack" (it was about the same length as a normal Jack, but about the same across and all muscle, and bred for dog fighting in the Essex tradition of "Put two dogs in dustbin and sit on lid. The one that comes out alive wins") was known to eliminate full grown foxes. But you may need more than one dog because Weill's disease can take dogs too.

There is at least one 'catter or ex-catter who used to work in ratting, with two Jack Russells and an unlicensed .22 rifle.