I come from what is probably an upper-working class background. My parents don't like classical music but i love it, especially Handel, Rameau, Albinoni, Corelli and Bach - i'm a baroque boy! But then i love classic literature and (while i know nothing about it) art as well so i'm unmistakably middle-class in my tastes.
While concerts may be quite expensive to see, CDs/downloading classical music is relatively inexpensive so there is nothing physically stopping people from a lower income background enjoying classical music. maybe it's the mere association people have with classical music and stuffy, uptight middle/upper-class people - they judge the music based on its traditional audience rather than the music itself.
But i'm of course making generalisations. i'm sure there are many people who enjoy classical music and who would also label themselves as working-class.