GW,
The guidelines for declaring an emergency, and their meanings are the same on this side of the pond. I doubt that we handle them any differently than you guys do.
The main difference that I've have seen in how emergencies are handled are usually dependant upon the controllers experience, and the pilots experience.
All the aircraft emergencies that I have worked the pilot usually calmly told me that he was declaring an emergency and what the problem was, so I consider myself lucky that I haven't had anything worse.