Green’s Dictionary of Slang

a member of the public, a customer.

2000		J.J. Connolly Layer Cake 24: She tells the Billy Bunter to take it home and [...] ‘totally cleanse it’.
2001		K. Sampson Outlaws (ms.) 35: In fact our regular Billies know full well that we are nothing other than the dearest firm around. [Ibid.] 96: The way it echoes round the station sends your everyday Billy Bunters scurrying for the food plaza until we’ve gone.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.