Poor households moving into social housing in Doncaster spend nearly a third of their income on rent, according to official figures.
Housing charities said a reduction in benefits has made the rent burden more severe for people in need and called for more social homes to be built to keep up with demand.
The latest data from the Ministry of Housing, Communities and Local Government shows that new social tenants spent, on average, 30% of their monthly income on rent during the financial year 2017-18.
Although it is 72% cheaper than the private market, the median tenancy rent for social houses in Doncaster was £75 per week.
This amount excludes the payments of bills.
Social housing is let at low rents to those who are most in need or struggling with their housing costs. Councils and not-for-profit organisations, such as housing associations, are the main providers.
According to the housing charity Shelter and the Joseph Rowntree Foundation, spending more than a third of your disposable income on rent or a mortgage means you may not be able to afford other basic needs.
Nationally, households living in social housing spent 34% of their income on rent.
The median rent for new social housing tenancies in England was £83 per week, which is £1.50 lower than the previous year. The data shows that 25% of new social housing tenants were in work in Doncaster.
A further 8% were over 65 and 10% were rough sleepers or people living in temporary accommodation.
Catherine Ryder, head of policy at the National Housing Federation, said: "Our research shows we need to build 90,000 homes for social rent each year to keep up with demand.
"To do this, Government must reform how land is sold, so that housing associations are not directly competing with private developers for land to build social housing.
"Reduction in benefits since 2010 will also have had an impact on people's incomes and are making it much harder for people to afford rent and other essentials."
In 2017-18, 2,650 new social houses were added to the housing stock in Doncaster, 78% of them owned by the local authority and 22% by housing associations.
Nationally, there were 313,000 new social housing lettings in 2017-18, a 6% decrease on the previous year.
The total number of new social housing lettings peaked in 2013-14, and since then there has been a steady downward trend.
A spokerperson from the ministry puts this trend down a fall in the number of vacant properties available to be re-let. He said: "A widening affordability gap between the social and private rental sectors discourages current social tenants from moving into private accommodation. As a result, turnover is lower."