There is an interesting story about the relationship between Igor Stravinsky and the Hollywood film industry. When Darryl Zanuck decided to make a movie out of Franz Werfel's novel, The Song of Bernadette, Werfel lobbied heavily for Stravinsky to compose the score. He got his wish. However, the rest of the story can be found on IMDb as follows:
The movie's original score was partly composed by famous composer Igor Stravinsky but was subsequently rejected in favor of Alfred Newman's score. When Stravinsky was invited to a screening so he could plot out his score, he replied that he'd already begun. Evincing an unwillingness to change what he'd already composed, he was released from his contract. The second movement of his Symphony in Three Movements evolved out of the unused score.
This is the closest Stravinsky ever got to actually composing for the Hollywood moguls, although, as the hyperlink to his name demonstrates, his compositions have been appropriated for a wide variety of films (my personal favorite always being the adoption of some of his Soldier's Tale music in the film version of The Balcony).
Beyond these appropriations, however, is the work of film composers who tried to capture the "Stravinsky sound" for their own devices. As I recently wrote on Examiner.com, Bernard Hermann did this particularly effectively in his music for the opening credits of Alfred Hitchcock's Psycho (one of those fine points that did not make it to the IMDb Trivia page for this film). However, the Bernadette music was a product of Stravinsky's neoclassical period; and composers who tried to "fake" the neoclassical Stravinsky are harder to find.
Today, however, I found one; and he is a perfectly respectable composer in his own right. He is Richard Rodney Bennett, and his labors constitute the score for the television movie John Schlesinger made of The Tale of Sweeney Todd. My inclination is to view this as a sincere (if somewhat concealed) homage on Bennett's part; and I believe it is related to a key way in which Schlesinger's conception differed from the Stephen Sondheim musical (which has now migrated to several opera houses). The Sondheim version is set in the physical and moral filth of Industrial Age London, hence his decision to welcome the audience with that blast of a hideous steam whistle. Schlesinger, on the other hand, opted for an earlier time, which is basically that of the London captured by William Hogarth. In other words this is the London of Hogarth's Rake's Progress, the basis for Stravinsky's only full-length opera. Whether or not the rights to this music were available, there is no way that it would have fit in with Schlesinger's conception of the narrative; so I would guess that Bennett was tasked with capturing the spirit of that opera with incidental music that would better serve Schlesinger's contexts. Bennett achieved his task with both success and subtlety. Stravinsky is, indeed, honored by his efforts, but in ways that only hard-core Stravinsky addicts will grasp and enjoy. Everyone else can rest content with the penny-dreadful effects and Ben Kingsley at his most sinister. Also, unless I am mistaken, the references to The Rake's Progress are complemented with a few nods to that Symphony in Three Movements, almost as if to reassure Stravinsky's spirit that his efforts finally conquered the silver screen.