Which classical composers most influenced The Beatles?

None of the Beatles had a background in classical music. Paul McCartney's (jazz musician) father would turn the radio off if a classical record came on.

Bach's Bourrée 

George did, however, learn one classical 'party-piece' in his early teens, which he then taught to Paul. Neither knew the title, but they vaguely knew it was by Bach. They later learned it was the Bourrée from the E minor Lute Suite.

Paul also discovered that they had been playing the piece inaccurately. This ultimately proved to be a happy accident. McCartney's variation on the Bourrée would be the starting point for one of his most admired songs.

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