More than 12,000 people have moved into work after being told about the benefits cap, the government says.
The cap, on the total amount of benefits that non-working people aged 16 to 64 can receive, has begun rolling out across England, Scotland and Wales.
Couples and lone parents will now not receive more than £500 a week, while a £350 limit applies to single people.
But critics say the changes will hit parts of the country unfairly, and will not tackle underlying problems.
Those in work who also claim benefits, are not affected by the cap.
"What the job centre staff have told us is that they've seen a genuine increase [in people looking for work] since they've alerted people that they're likely to be in the cap," said the Work and Pensions Secretary Iain Duncan Smith, who has spearheaded these changes.
He argues the current level of benefit discourages people from looking for work.
"We will always be there to support those who need help but the days of blank cheque benefits are over," he said.
The Department for Work and Pensions (DWP) said that 12,000 claimants had found jobs over the last year, after being contacted by job centres.
The job centres warned them they might have their benefits capped if they did not find employment.
Key payments including jobseeker's allowance and child and housing benefit count towards the cap.
The Department for Work and Pensions estimates about 40,000 households will be affected.
Critics say the cap fails to tackle underlying issues, such as the difficulty of finding work, the cost of housing and regional differences.
The National Housing Federation (NHF) agrees with the principle that those on benefits should not earn more than those in work, but it argues that the cap does not work in London and the south-east, where rents are high.
Those affected by the cap have their housing benefit reduced.
"In many parts of the country, families won't be able to pay high private rents because of the cap," said Ruth Davison of the NHF.
"There will be more demand for than ever for affordable housing, particularly in Greater London where nearly half (49%) of the people affected by the benefit cap live."
The cap will be completely implemented by 30 September, and will then become part of the Universal Credit system.
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The cap, not yet law in Northern Ireland, is said to reflect the average working household income.
It has already been implemented in four London boroughs - Haringey, Enfield, Croydon and Bromley - since April.
The benefits cap applies to people receiving jobseeker's allowance, child benefit, child tax credits, housing benefits and other key support from the government.
There is no cap on people who receive Disability Living Allowance or its successor, the Personal Independence Payment, as well some other benefits, such as industrial injuries benefit or a war widow or widower's pension.
"The benefit cap returns fairness to the benefits systems," Mr Duncan Smith said. "It ensures the taxpayer can have trust in the welfare system and it stops sky-high claims that make it impossible for people to move into work.
"The limit of £500 a week ensures no-one claims more in benefits than the average household and there is a clear reason for people to get a job - as those eligible for Working Tax Credit are exempt."
About £95bn a year is currently paid out in benefits to families of working age.
The government hopes the cap will save about £110m in the first year, and £300m over the next two years.
The four local authorities where the cap has been introduced say they are struggling to introduce the measures.
One of them, Haringey, said it was given £1.8m by the government in the first year, to help with the transition, and ease cases of hardship.
But it estimates that this year alone it will have to add £2m of its own money to pay for the changes, which it said is not sustainable in the longer term.
One alternative is for families to move to areas where housing costs are lower.
"We will have to consult on what that means on potentially requiring families to move outside London, which I think is very difficult," said Claire Kober, the leader of Haringey Council.
Rebecca is a Sunday school teacher in Haringey, who may be affected by the cap when transitional support runs out.
She told the BBC she would not want to move away.
"I think moving out from my community....my community will be missing me. If they move me out, I will start from zero," she said.
Geoff Parker-Chance, from Clacton in Essex, has worked for most of his life, but has been claiming benefits for the last year.
He believes the new system is unfair.
"The cap is outrageous," he told the BBC. "It seems unfair that I contribute, but when I need it, it gets taken away."