Currently, copyright law in Britain puts the expiration date of copyright at 70 years from the death of the author. (The same holds true in America, although it's 120 years from creation/95 years from first publication for works for hire, although that isn't germane in this particular case for reasons that should become obvious shortly.)
Sax Rohmer, creator of Fu Manchu, perished in 1959. This means that in 2029, a relatively short sixteen years from now, Fu Manchu will go into the public domain. (unless his Fu Manchu novels were done as work for hire, which means that the copyright wouldn't expire any later than 95 years from 1913, date of publication of the first Fu Manchu novel. Since Fu Manchu didn't go into public domain five years ago, I think we can assume that it wasn't work for hire.)
My possibly interesting question is: Do you think that people will make use of Fu Manchu once the character becomes public domain? On the one hand, the "Yellow Peril" stereotype, which Fu Manchu exemplifies and arguably created, is at this point an embarrassing legacy of an era in which racial stereotypes were common and accepted. Pretty much any story involving Fu Manchu, in any medium, is going to be analyzed with a very skeptical eye by anyone who has any interest in racial sensitivity. These days, that's a lot of people (which is something I'm tremendously heartened by, honestly.)
On the other hand, modern sci-fi/fantasy is a descendant of the pulp novels like the Fu Manchu series, and in some ways is inextricably linked to them right at the roots. Anyone trying to make a serious exploration of the racial politics of cult fiction has to take the Yellow Peril stereotype into account, and if you're going to do that, what better symbol to use than the original Yellow Peril himself? (To say nothing of those people who just can't resist making use of an iconic character simply because he is an iconic character. There's already been at least one "Fu Manchu Versus Sherlock Holmes" novel, and I can imagine that it might be hard to resist the temptation to do a Fu Manchu/Dracula team-up, or a "Fu Manchu and the Cult of Cthulhu" story.)
I do believe there will be some use of the character starting in 2029; but given the problematic nature of the character, I'll be very interested to find out how much.