One of the things I liked best about the film was the abundance of folk music. For those who care, the screen adaptation was written by Noel Langley, who was one of the screenwriters for "The Wizard of Oz". Here are the songs in the soundtrack, as listed at Internet Movie Database, though they seem to think it ends with "Silent Night":


"Hark the Herald Angels Sing"
Music by Felix Mendelssohn-Bartholdy
Sung by offscreen chorus during opening credits


"Sir Roger de Coverley"
Traditional
Played by fiddlers at Fezziwig's Christmas party


"Barbara Allen"
Traditional
Played as background music during film and sung by guests at Fred's Christmas party


"Silent Night"
(excerpt)
Music by Franz Gruber
Sung by offscreen chorus at end of film


"My Love's an Arbutus"
Music by C.V. Stanford
Heard instrumentally as background music during all scenes involving Alice


"The Lincolnshire Poacher"
Traditional
Whistled by Jack Warner


"Oranges and Lemons"
Played when Scrooge meets the Spirit of Christmas Present