Twenty years ago, a British person would, indeed, have said “cell [or cellular] phone”. That seems to have changed, and now “mobile” seems to have become much more common. However, I suspect most Brits would still understand “cell phone” perfectly well (and even without all the exposure they get to American entertainment media).
In fact, most of the examples in this thread seem to be phrases that would both be considered perfectly normal in one country, but only one of which is common in the other. Rather surprisingly, to my mind, the country that most often seems to accept just one variant appears to be America. Over in another thread, in GQ, I am surprised to find myself being assured that Americans would never say “Happy Christmas” rather than “Merry Christmas,” although I (backed up by others in the thread) know quite well that both forms are common in Britain. I find the apparently greater linguistic restrictiveness of the U.S. odd, considering that America is much the larger, and, in most respects, the more culturally diverse country.
While I'm here, I would like to mention that the word "nervy" has almost opposite connotations in Britain and America. In Britain, a nervy person is one who is very prone to nervousness, someone timorous and easily rattled; in America, a nervy person is one with "a lot of nerve" (in a good way), someone bold and willing to take risks. (I realize that, as a single word, this does not fully meet the conditions of the OP, but it is a rather radical difference - one that could lead to real misunderstandings - that seldom seems to be remarked upon.)
Also, many British people (including, once, myself), presumably having heard the American expression "fender bender," believe that "fender" is the American word for what they themselves would call a car's *bumper*. It is not. A bumper is a "bumper" on both sides of the Atlantic. *Fenders*, in America, are those parts of a car's bodywork that partially cover the wheels, protecting them from the elements (and, like bumpers, they do rather often get bent during minor accidents). I do not think British English actually has a word with quite the same meaning, although the rough equivalent on a bicycle would be called a "mudguard" (I am not sure if that is what it is on an American bike).