Mr. P: "Whom did you give the letter?" must indeed be AmE. I've been keeping an eye on this thread and wondering what all the fuss was about!
"To whom did you give the letter?" and "Who(m) did you give the letter to?" are derived from "I gave the letter to whom."
So, with Casi's incorporation transform in mind, why in the world would not "Whom did you give the letter?" be derived from "I gave whom the letter."?
Likewise with "the person whom I gave the letter" - also bothersome to the non-American ear?