I think that there have been well written socially aware fiction books.
I think several of the books of this century highlighting the plight of black americans in the semi-apartheid of the 50s and 60s are interesting. A small island was one of these, although written from a UK perspective, of how unwelcome the immigrant community was made to feel when arriving here.
Monica Ali's Brick Lane, although quite light reading, chronicles a quite passable view of second/third generation immigrants to London's East End.
What about Bonfire of the Vanities - a tale of two cities really!
Angela's Ashes - depicts life in Ireland, when social support for those in poverty was non-existant and life unremittingly harsh.
Philidelphia as Aloha has just said.
If we are getting heavy, Solzhenitsyn with his view of life behind the Iron Curtain, is a worthwhile read. I 'enjoyed' Cancer Ward too.
A quick search on Amazon looking at fiction and environment, brings up a plausible list of books some of which look like a good read!
Is perhaps the opposite true - that in fact there are so many good writers, writing about socially relevant matters, that one of them does not stand out in the way that Dickens did in his day? Perhaps fiction writers at that time were less willing to offend the sensibilities of their readers (who would have been primarily middle/upper class) by revealing too much about how gritty life was for the underclasses.
I also have to say, that whilst I appreciate Dickens for the writer that he was, I'm nevertheless no great reader of his books!