Imposing a nationwide cap on benefits will "encourage people into work", the government has said, as the plan is rolled out in four London boroughs.
Couples and lone parents in Haringey, Enfield, Croydon and Bromley will not receive more than £500 a week while a £350 limit applies to single people.
But critics said the cap failed to tackle underlying issues, like the cost of housing and regional differences.
The cap will be imposed across England, Scotland and Wales from July.
Jobseeker's allowance, income support, child and housing benefit count towards it, but not Disability Living Allowance.
The cap, which is not yet law in Northern Ireland, is said to reflect the average working household income.
Ministers say welfare spending needs to be reduced and they claim that the threat of the introduction of the cap has already spurred 8,000 claimants who would have lost out to find jobs.
Speaking on the BBC Radio 4's Today programme, employment minister Mark Hoban said that if people want to escape the benefits cap "the best way to do it is to move into work".
"I think what people want to see is a benefit system that's fair, that's affordable, that encourages people into work and these reforms help deliver that," he added.
And, in a message on Twitter, David Cameron hailed "a big day for welfare reform as we pilot a cap on benefits equal to the average wage" - adding "amazingly Labour oppose it".
Jobseeker's allowance, income support, child benefit and housing benefit are on a long list of payments which count towards the calculation of the cap, which is expected to see cuts of about £90 a week on average for the 40,000 households affected.
Sarah Burns, a single mother, told the BBC she would lose about £90 of the more than £500 she receives every week.
She said: "Obviously we will have to cut down on shopping bills. And we'll have to cut our use of gas and electricity. It's really that serious.
"Activities that the children do, like school trips and scout cubs, I probably won't be able to afford anymore."
People on Disability Living Allowance (and the Personal Independence Payment replacing it) will be among those exempt from the cap. To encourage people to seek work, ministers have decided that people with a job who receive Working Tax Credit will also not be affected.
The Department for Work and Pensions says about £90bn was paid out in benefit payments to people of working age and their families in 2009-10. It hopes the cap will save about £110m a year.
Business Secretary Vince Cable told BBC Radio Tees that he believed "most people" agreed with the "basic principles" of the changes - that no-one should be getting more in benefits than the average wage of someone in employment.
But he added: "These reforms are very controversial and some people are going to get hit unfortunately.
"Inevitably you will get hard cases. You have to create some support for the hard cases so we don't have real difficulty".
Labour leader Ed Miliband said the welfare bill was rising not falling.
"The first thing the government should be doing to reform welfare is to put people back to work and offer people real jobs with real responsibilities," he said.
"We've said we're in favour of a benefit cap but it has got to be adjusted regionally depending on housing costs in each region. The danger of the way the government is doing the cap is that it forces people into temporary accommodation, bed and breakfasts, which drives up costs not reduces them."
Gingerbread, a charity which campaigns on behalf of single parents, said it was "deeply concerned" about the impact the cap would have on families and communities.
"The cap doesn't begin to tackle the underlying problems of the shortage of low-cost social housing," it said.
"We fear that many children will be pushed deeper into poverty or uprooted from their communities, schools and family networks as a result."
The TUC said it was wrong to suggest the cap had spurred people into finding work and it was asking the statistics watchdog to determine whether ministers had "misused" information.
"The government's own analysts say that 16,000 fewer people will be affected because ministers have changed the rules about who is eligible, not because of any change in behaviour," said its general secretary Frances O'Grady.
And Jonathan Portes, director of the National Institute of Economic and Social Research and a former chief economist at the Department for Work and Pensions, said there was "no evidence at all" that the cap had affected people's behaviour.