The Firebird - Finale Igor Stravinsky
This image appears in the gallery:
The best BAFTA-winning soundtracks
John Williams has a similar record at the BAFTAS as he does at the Oscars - basically, he's the one to beat. He has enjoyed countless nominations and several deserved wins, of which Jaws was the first in 1975 (along with his score for The Towering Inferno).