Football is still very much a working class sport, maybe not at the ownership level, but certainly with regards the players. In fact I'd say that people from more privileged backgrounds are often made to feel a bit odd in football. Graeme Le Saux got mocked for being 'posh' and I remember early on in his career people used to criticise Kaka's motivation versus his compatriots and rivals because he'd had a financially comfortable upbringing and hadn't had to battle his way out of slums like some Brazilian players.
If we were going to criticise any sport for elitism it would be golf or F1 that would immediately spring to mind, not football.