Larger families claiming benefits, many with members in work, will be unable to afford increased rents on social housing across swaths of urban England, according to research. Rents will rise to as much as 80% of those in the private sector.

The government wants the cash to be used to build affordable homes, to make up for a significant reduction in grants. But with private sector rents in England having risen to 58% of the gross weekly wage of the lowest paid, and to 72% in the case of London, there are fears many on benefits will be unable to afford the impending increases.

It has been feared that the move would hit families with three or more children living in London. But the research, by Cambridge University academics, indicates that the new market-pegged social rents will be unaffordable for families with three or more children in many parts of the country. The investigations, by the Cambridge Centre for Housing and Planning Research, suggests a couple with three or more children would breach the maximum £26,000 benefit cap in four out of the five local authority areas it examined.

The four authorities were: Brighton and Hove, East Sussex; Bromley, Greater London; Hertsmere, Hertfordshire; and Mid Sussex, all areas that are home to large numbers of families in affordable housing. A couple with three children in Hertsmere would face a shortfall of £56 a week if 80% market rents were charged, while in Brighton and Hove the shortfall would be £34.

The only place in the study where 80% rents could be sustained by a larger family dependent on benefits, without incurring additional hardship, was Plymouth.

"We don't believe that increasing rents to 80% of market levels across the board is appropriate," said Keith Exford, chief executive of Affinity Sutton, one of the country's largest social housing providers, which commissioned the research. "It could cause acute financial and affordability problems for new residents and this research demonstrates it will not work for larger families."

Housing providers could charge less than the 80% rate – and several have indicated they will do so for larger families. But it is estimated that, even if families only pay the expected 60% to 65% of the local market rate, those who depend on benefits will struggle.

"Most people living in our accommodation in inner London are working, often in part-time or insecure jobs." Exford said. "They can't afford to commute to the jobs and public transport is not available at 4am in the morning when they are coming in to clean offices. Do we want whole sections of our cities to be like Paris, only for the rich?"

Christine Whitehead, who led the research, said the findings suggested there was a dilemma ahead for those providing social housing. "The big question now is, who is to be housed under the new regime? The low-income employed or those who will need housing benefit to pay the increased rents?"

Alex Fenton, who carried out the modelling for the study, warned: "We should treat this scheme with caution. There are still big questions about whether more houses will get built as a result."

• The coalition's plans to reform benefits could see one in five Liberal Democrat voters deserting the party. A poll for the National Housing Federation found that 20% of those who voted Lib Dem in 2010 would be less likely to do so at the next election. The proposals have caused much concern among the party's backbenchers. In February, the government had to drop its proposal to cut housing benefit for those who have been unemployed for more than a year.