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
Orlando Bloom has visited children whose school was destroyed by shellfire during the conflict in Ukraine.
Jeremy Corbyn has launched a fresh attack on "ideological" Conservative cuts ahead of Thursday's elections.
Daddy Day Care star Eddie Murphy is celebrating the birth of his ninth child.