Claimants in the London boroughs of Haringey, Enfield, Croydon and Bromley are the first to face a cap on their benefits.
Employment minister Mark Hoban said it was "only fair that those who are on benefit face the same choices" as those in work.
But shadow minister for disabled people Anne McGuire highlighted the "major issue of imposing that level of benefit cap in London, where the biggest factor in benefits is actually the high rents."
Political correspondent Libby Weiner reports:
More top news
Justice Secretary Michael Gove warned David Cameron that his failure to limit migration is 'corrosive' to public trust.
After a lively start to the long weekend with torrential, thundery downpours - a drier night.
Real Madrid have clinched a record 11th Champions League title after a dramatic penalty shoot-out victory over Atletico Madrid