The documentary, which aired on Monday night and depicted the lives of residents of James Turner Street in Birmingham, sparked hundreds of complaints to broadcasting watchdog Ofcom and Channel 4 about how it portrayed people on benefits.
Some residents claimed they were tricked by film-makers into taking part.
But Channel 4 insists it was "very clear and transparent" with those taking part about the nature of the programme it envisaged.
Dame Anne Begg, Labour MP for Aberdeen South and the chairwoman of the House of Commons Work and Pensions Committee, said the introduction to the show said it would portray life on a street where three-quarters of residents were on benefits, but then focused almost exclusively on people receiving unemployment benefits, which make up only a small proportion of the overall social security bill.
"What struck me is that it was called Benefits Street and then three-quarters or more of the programme actually followed one storyline which was about a petty criminal and shoplifter and how he lived on the proceeds of his crime, rather than the reality of what people face when they live on benefits," Dame Anne told BBC Radio 4's Today programme.