Both the IMDB and Wikipedia list Gerard Schurmann as the composer of a 1948 British film called BUT NOT IN VAIN. But Schurmann's own website contradicts this, giving his first film as 1956's THE LONG ARM (THE THIRD KEY). The fact that BUT NOT IN VAIN is considered a lost film by the BFI suggests that this matter won't be cleared up anytime soon.
He may not beat Previn, but I just wanted to put in a plug for Gerald Fried (most famous for Paths of Glory and The Killing). His earliest credit is 1951's Day of the Fight a documentary short. His first feature is Kubrick's Fear and Desire 1953.