1. The word “cheerio” does not precede 1910, and furthermore it has been obsolete for some time now, and not because it was pushed out by an Americanism.
2. The Brits are correct to insist on “I couldn’t care less,” rather than the American “I could care less.”
3. Americans used to call an umbrella a “bumbershoot,” yet nowadays if they hear the word they often think it is a Britishism. The British slang term is in fact “brolly.”
4. When Americans speak, they prefer “repetitious” over “repetitive,” even though the latter is nine times more common in American text. Perhaps repetitious is more…repetitious.
5. “One-off” is a Britishism that largely has caught on in America.
6. How can they call it “rumpy-pumpy”?
7. “The British use sorry at the rate four times the Americans do.”
All that and more is from the new and fun book The Prodigal Tongue: The Love-Hate Relationship Between American and British English, by Lynne Murphy.