The benefit cap has been implemented in 4 London areas, the Department of Work and Pensions (DWP).
In total, just over 2,400 households were capped in the boroughs of Enfield, Haringey, Bromley and Croydon, DWP figures reveal.
Nationally since April last year, Jobcentre Plus has moved 12,400 of those claimants potentially into work and 32,300 have accepted employment support.
Secretary of State for Work and Pensions Iain Duncan Smith said: "The limit of £500 a week ensures no-one claims more in benefits that the average household and there is a clear reason for people to get a job - as those eligible for Working Tax Credit are exempt."
The cap limits will be set at £500 a week for couples, with or without children, and lone parent households, and at £350 a week for households of a single adult with no children.
"Universal Credit will build on this, so claimants will know they are always better off in work on their own 2 feet than sticking on benefits."
From 15 July the national roll-out of the benefit cap will take place to cover an estimated total of 40,000 households limiting benefit payments to £500 a week or £26,000 a year.
The cap will apply to combined income from the main out-of-work benefits:
•Jobseeker's Allowance
•Income Support
•Employment and Support Allowance
•other benefits such as Housing Benefit, Child Benefit and Child Tax Credit
The benefit cap will not affect a household if a member is entitled to Working Tax Credit.
All households which include somebody who is receiving Disability Living Allowance will be exempt as will those who receive a War Widow's or Widower's Pension.
The benefit cap will not be applied for 39 weeks to those who have been continuously in work for the previous 12 months.
