The benefit cap – according to opinion polls the government's most popular welfare policy – is neither forcing unemployed people to take a job nor saving taxpayers' money, according to the first in-depth study of the policy.

Research in the borough of Haringey in north London found just a handful of the 747 households affected by the cap have secured a job or increased their working hours since it was introduced six months ago, despite intensive and personalised support from councils and local jobcentres.

Although the policy was shaving £60,000 a week from the benefits bill locally, this amounted to just 1% of the council's total weekly benefit expenditure. Haringey has so far spent £55,000 a week on short-term discretionary grants to help claimants affected by the cap meet rent shortfalls, and thousands more on providing extra welfare and employment advice.

The few capped claimants who had so far moved into employment were already "close to the labour market" and were likely to have got a job anyway, or were already working part-time and had increased their hours, according to Haringey jobcentre officials and charity job advisers interviewed by the Chartered Institute of Housing (CIH).

CIH chief executive Grainia Long said: "The government said the benefit cap would save money and encourage people into work, but this report shows it is far from achieving those aims in one of the worst-affected areas."

A spokesperson for the Department for Work and Pensions (DWP) insisted the benefit cap was "definitely helping" some of those affected to get into work, although it recognised some individuals may take longer to move into employment.

The benefit cap limits the amount any working-age household can receive in benefits to £26,000 a year, or £500 a week (£350 for those without children). In Haringey, over half of households affected were losing between £50 and £200 a week. Some 2,383 children are in families affected by the cap, while a third of capped households have more than four children.

Polling suggests a majority of the public approve of the cap, which is set at the median income of a working family. But the government has struggled to prove that it works. In July, work and pensions secretary Iain Duncan Smith controversially said he "believed" the threat of the cap prior to its introduction had persuaded more jobless people back to work, but was unable to produce robust statistical evidence to support his claim.

Fears of mass evictions of claimants, or displacements to cheaper areas outside London, have not been realised, says the CIH report. However, it warns that many capped families are dependent on the council's short-term discretionary support fund to meet their rent, and when this runs out, vulnerable claimants who cannot find work are likely to become homeless.

The report found that the cap had caused serious disruption and hardship to some vulnerable households, as well as triggering some unintended consequences.

Researchers came across "several reports" of women choosing to stay with violent partners who had a job, because they believed that if they took the children and left the family home they would be subject to the benefit cap.

One Haringey school reported that seven children had left because of the cap as a result of families moving away to cheaper housing, and that it "expected more to follow".

Most of the 25 capped claimants interviewed for the study reported degrees of stress, sleeplessness and depression. One told researchers that she had attempted suicide. "It is likely that many of these people had existing underlying problems, but these are likely to be worsened by the additional issues raised by benefit capping," the report says.

Ill-health, lack of skills, education, and "job readiness", coupled with the cost and lack of availability of childcare were the most "significant barrier" preventing many of those affected from getting a job, the report found.

Claire Kober, leader of Haringey council, said: "This research shows that the benefit cap has failed in its main objectives. Only a few households have been able to get back into work and, while the government may be making some savings, the real costs are just being passed to local councils already under enormous financial pressure."

The benefit cap was initially estimated to affect 56,000 households nationally. This was revised downwards to 40,000 earlier this year. Roughly half of these are in London, where an estimated 7,000 families will lose more than £100 a week.

The Labour party says it supports the benefit cap in principle, but would introduce regional variations so that benefit caps would be set higher in areas like London.

Haringey was one of four areas that piloted the benefit cap from April. All other English, Scottish and Welsh local authorities have since introduced the cap.