Several other commentators have mentioned the British soaps - Eastenders, Coronation Street, Brookside (now defunct), Emmerdale etc. All of these are overwhelmingly about the working classes and these are also the highest rated programmes on British TV. The audiences for these are huge - before the audience fragmented due to the proliferation of TV channels, in the 'big' episodes (typically at Christmas) up to half the total population in the UK watched.
There are so many TV series or dramas centred around the working classes that I can't list them all - suffice it to say that it's very common and any US adaptation of a British TV show that mentions the use of working class characters (Queer as Folk, the Office - although I would say that many of the characters there were lower middle class - etc) the original British characters are also working class.
I also find it interesting that you identify cop shows as not being about a working class lifestyle because in many British cop shows (not all, but a sizeable proportion) I would say that what is depicted is overwhelmingly a working class lifestyle - take The Bill, for example.