Well, for starters, On Writing is now ten years old - good writing may not have changed in that time, but the publishing industry certainly has. I haven't read On Writing though (shame on me!), so I don't know what format he suggests.
I would agree that Britain and America differ somewhat. A lot of UK agents still want partials or sample pages to start with, not query letters. I also suspect that the "hard sell" approach would go down less well over here. The important thing is to be polite, professional and concise, and to summarise your book in a way that piques the agent's interest. Easier said than done, of course!
A bit of formality never hurts when you're contacting someone you've never met - "Dear Mr Smith" not "Hi Joe" as your email salutation, for example!