I can think of quite a few British shows - Eastenders, Coronation Street, Emmerdale and (to a lesser extent) Hollyoaks all have working class settings and characters. And although neither are still on there were kids shows like Grange Hill and Byker Grove, both about working class teenagers. Shameless has been mentioned a few times. Sugar Rush (about two teenage lesbians) has mostly working class characters. River City is only broadcast on BBC Scotland, but like Eastenders etc is about working class characters and lives, only this time in Glasgow.
And these are generally the most successful shows on British TV. Eastenders, Coronation Street and Emmerdale get higher ratings than any other shows.