A report published today by the Department for Work and Pensions (DWP) shows that 2,899 households have had their benefits capped since four early adopter authorities imposed the new limits on 15 April.
By the end of June, 85 per cent of the households affected had between one and four children.
And nearly three-quarters of the total number of capped households were made up of a single parent with a dependent child, or children.
The statistics show that more than two-thirds (69 per cent) of households lost £100 or less of benefit due to the cap each week. However, a total of 33 families lost between £350 and £400 per week.
The authority most affected by the cap was Enfield, which accounted for 48 per cent of the 2,899 households affected, followed by Haringey (26 per cent), Croydon (20 per cent) and Bromley (six per cent).
Tim Nichols, press and parliamentary officer at the Child Poverty Action Group (CPAG), said it was "disgraceful" that some 2,500 families with children had their benefits capped in the pilot alone.
"This isn’t solving problems, it’s just creating hardship," he said.
"The figures suggest that the cap is having a minimal impact in changing behaviours, but that is no surprise given that the families affected have few genuine choices.
"Employers who will take them on with the flexibility needed for their childcare commitments are scarce, and the affordable rents they need are simply not there.
"As time goes on and more areas are affected, we fear that many families are going to be made homeless, which costs the taxpayer a lot and is known to enormously affect the wellbeing of children and to cause them to fall badly behind at school.”
The benefit cap limits the amount of benefits that couples and lone-parent households can receive to around £500 a week or £26,000 a year.
The government argues this figure is the equivalent of the average household income after tax – or a gross household salary of £35,000.
National implementation of the benefit cap is being rolled out in two “tranches”.
The cap was introduced in local authorities where 275 or fewer households are predicted to be affected, on 15 July.
It is set to be introduced to local authorities with 276 or more households to be capped from next Monday (12 August).
Last month, The Children’s Society warned that twice as many children as adults will be affected by the cap. The society says 140,000 families with children will be hit by the new cap.