Families affected have seen their income drop by about £50 a week, the Department for Work and Pensions report showed.
It also stated the housing benefit of an increased 1,900 households had been cut by May 2017 compared to the previous quarter (Feburary 2017).
This was "because over the last quarter more households have had their benefits capped for the first time" - 15,000 had their benefits capped for the first time, although 13,000 moved off the benefit cap.
For most capped households the benefit cap is applied by reducing the amount of housing benefit they receive.
In the previous quarter (December 2016 to February 2017) 50,000 households were capped for the first time when the "main impact of the roll-out of lower cap levels to newly affected households was recorded", the report noted.
The lower benefit cap was introduced in November last year.
Between April 2013 when an initial cap was introduced and May 2017, a total of the benefit of 150,000 households were capped, the DWP showed.
The report also noted of those, 81,000 were no longer capped as of May this year, with 34,000 households having moved into work.
Since November last year, the benefit caps have been £20,000 outside of London and £23,000 in the capital. It was previously £26,000 across the country.
The figures drew criticism from housing groups and charities.
Terrie Alafat, Chartered Institute of Housing chief executive, said: “Homelessness has been steadily rising in all its forms since 2010 and we fear that the benefit cap could make things even worse.”
She said the loss of £50 a week was making it difficult for people to afford to pay bills, rent and possibly basic necessities.
Alafat noted that three-quarters of claimants are single parent families with young children who will find it “incredibly difficult” to escape the cap by finding work, given the cost of childcare and lack of flexible employment options.
She urged the government to rethink its welfare policies to ensure they were not getting in the way of people being able to afford to live in decent homes.
Katie Schmuecker, head of policy at the Joseph Rowntree Foundation, also highlighted the negative impact it has on single parents with pre-school children.
“It makes people who are already struggling poorer, while doing little to tackle the reasons that benefit spending is so high in the first place,” she said.
Adding: “The government’s own evaluation showed that the benefit cap has had only a small impact on people moving into work.
"This is perhaps not surprising given that those most affected have very young children.”
She too urged the government to act on the high cost of housing and called on the benefits cap to be scrapped.
Work and pensions secretary David Gauke hailed the benefits cap a “real success” because he said it had encouraged more people to get into work.
He added: “With record levels of employment and over three quarters of a million vacancies at any one time, even more people have the opportunity to change their lives for the better.”
