The phrasal verb has assorted meanings, most of them common to both British and American English: retain (“he hung on to his mother’s jewelry”), refrain from telephonically hanging up (Blondie’s “hanging on the tel-e-phone”), and remain clinging (the Supremes’ “you keep me hangin’ on”).
That leaves hang on is an imperative verb, metaphorically requesting or demanding a time out. The American equivalents are wait (a minute) or hold on (a minute); the OED quotes an 1841 dictionary of Americanisms describing the latter as “originally a sea phrase.” The OED’s first citation for this hang on is a surprisingly late definition in a 1941 dictionary of Australian (!) slang. But now it is so much a Britishism that I can’t even say it in my head other than in my lame British accent (believe me, you don’t want to hear).
All the more reason why the American chattering classes seem to be lapping it up:
... spelling out that members of Congress shouldn’t use non-public information gained through their jobs to line their pockets? As Financial Services Committee Chairman Spencer Bachus allegedly did, according to a 60 Minutes investigation? That’s more in the category of hang on, I can’t believe this is not already against the rules. (Andrew Rosenthal, New York Times, January 27, 2012)
Scientology appears to be giving you the promise of a better knowledge of God, perhaps an attractive prospect for youngsters who might be feeling that more mainstream organized religion leaves them cold. But hang on a minute. What “god” do Scientologists believe in? (Villagevoice.com, February 7, 2012)
notoneoffbritishisms.com 
Whoa, hang on a second. This is a Britishism? I hear it all the time in the US, and always have done. (Now that’s a Britishism – “have done.”)
I have to agree with the earlier commenter. I’ve used “hang on!” imperatively for my whole life. I would say the BrE and AmE uses converge.
That makes three of us. I wouldn’t have thought of “hang on!” as a Britishism. I do agree that “hold on!” is more common, though.
Me, four.
Brits would also say “hang about!” to have the same meaning. I have a suspicion that this is a cockney usage. Is this also accepted usage in US?
Me, five.
Fun Fact: Blondie’s Hanging on the Telephone was first recorded by The Nerves, a never-quite-made-it band who also had on its staff Peter Case (Plimsouls) and Paul Collins (The Beat). Talk about your 80s-Power-Pop ancestry!