Here's a few Aardman shorts that have used library music. Most of these can be found on the UK Aardman Classics DVD.
Confessions of a Foyer Girl:
? (Leadup to title card)
Film Opener - Paul Lewis [Studio G] (Ending)
Palmy Days:
By the Sleepy Lagoon - Eric Coates [Chappell] (Opening; Ending)
War Story:
Pageantry Processional - Ronald Hanmer [KPM] (Title card)
Calling All Workers - Eric Coates [Chappell] (Bill Perry describes how he reacted to the Blitz)
Acts of Heroism (c) - Trevor Duncan [KPM] (Credits)
Owzat:
Palm Court - Paul Williams, Kurt Briggs, Aaron Briggs [Amphonic Music] (Credits)
Stage Fright:
Roses and Moonlight - Alan Moorhouse [KPM] ("Who says you can't teach an old dog new tricks?")
Al Dente:
Neapolitan Mandolin - Alessandro Alessandroni [Chappell] (Start of the short; Waiter brings out a vegetarian meal)