Dystopian; Science Fiction; Drama
Although there aren't any aliens, black holes, or time travel, A Clockwork Orange is in a similar dystopian sci-fi genre as Brave New World. (Plus, its fashions are from another galaxy.)
Both take place in a world similar to—but not quite the same as—ours at some point in the near future. A Clockwork Orange has drug-laced milk that increases young thugs' capacity for crime. People are scared to leave their houses. Suspenders are in.
But don't make a 1:1 comparison—A Clockwork Orange is different from Brave New World because this isn't a utopia gone wrong; it's society on a downward slide.