Mamyalynne, Shakespeare in King Henry VI wrote about "a fall off of a tree."
Richard Steele in The Spectator wrote, "I could not keep my eyes off of her."
Mark Twain in Huckleberry Finn wrote, "I'll borrow two or three dollars off of the judge."
Clearly, "off of" was a common structure in the past and on both sides of the Atlantic. Nowadays it may just be a colloquial or dialectal form here in Britain, but it is obviously still going strong. It may not be 'standard', but it is perfectly acceptable and not a heck of a lot different from "out of", really.