I thought it was a fair portrayal all round really; the housing officers are doing a horrid and thankless job and people really are suffering. There didn't seem to be the 'look at the freak show and be outraged' aspect that seems to be what Benefit Street and other such programs go for.
I'm not entirely comfortable with people being moved out of London (especially children from settled schools, what if you have a child with severe learning difficulties?) It does seem unfair and that you're penalised for being poor. That said, I do think if you're in a vaguely decent situation financially and house wise, you do have to consider how many children you have too; the couples that had respectively seven and nine children were not in that great a place to start off with and I do think it's a consideration you have to make when you bring a child in to this world as they also suffer. Also the lady who would rather do volunteer work and study than what the council suggested to her was, in my opinion, feckless and short sighted.
I do wonder what the long term effects might be; what happens when Birmingham gets full for example, does this create some sort of ghettto? Not sure.