The writer of the novel, 'Anthony Burgess' , claimed that the term "clockwork orange" was a Cockney phrase, but most philologists agree that there has never been any such phrase until the appearance of his book. Burgess lived in Malaysia during the 1940s, and the Malay word for man is "orang", from which "orangutan" (man of the jungle) is derived. There is, however, an English slang expression for a gambling device known as the "one-armed bandit" in the U.S.: a clockwork fruit (the gambling device typically is referred to as a "fruit machine" in the UK due to the depictions on its dials; clockwork in England is a word applied to a plethora of mechanical devices beyond just time-pieces). The anthropomorphic look of a "fruit machine" (thus, its name "one-armed bandit" in the U.S. for its roughly man-sized shape and "arm" giving it a humanoid appearance) may well have given rise to the term "clockwork orange" in Burgess' fertile mind as Alex, through conditioning, is turned into a robot (which a fruit machine resembles). Gambling also is a game of chance, and Alex literally is gambling with his soul. This is made explicit, particularly in the film, when Dr. Brodsky tells Alex -- who is upset over the use of Beethoven on the soundtrack to the atrocity films and claims he has been enlightened -- to take his chance, as he will be free in a fortnight (roughly the time an annual vacation in an English resort such as Blackpool -- the Las Vegas of Britain -- with its scores of fruit machines, would take). The writer of the book, 'Anthony Burgess' , lived for a time in Malaysia. After returning to London his wife was assaulted by four American GI's during the black-out, thus giving inspiration to this story. In Malay, the word "orang" means man, [this is also part of the derivation of the word 'orangutan', the other half being derived from "hutan" meaning jungle] therefore, the title of the story is actually a pun on the British expression. Rather than a clockwork fruit, it is a clockwork man, which is, of course, exactly what Alex has become by the end of the film.
From the IMDB. "Welly, welly, welly, welly, welly, welly, well."