Waverley was one of a few areas in England where the number of new social lettings has risen over the last 10 years, new figures show.
It comes as the number of new social home lettings across England fell by more than a third over the last decade.
The Institute for Public Policy Research said there was "clear unmet need for social homes", and building more would help combat the housing crisis and reduce child poverty.
New figures from the Ministry of Housing, Communities and Local Government show 412 households secured social home tenancies in Waverley last year.
This includes general needs housing, which are not designed for a specific occupant, and homes designed for specific types of people, such as the elderly or those with disabilities, called supported housing.
This was an increase on a decade ago, when there were 357 new lettings in 2013-14.
This makes Waverley one of only 42 local authority areas where the number of new social homes has increased from 10 years ago.
Across England, the number of new tenancies starting annually has fallen from 396,000 in 2013-14 to 261,000 last year.
Matt Downie, chief executive of homelessness charity Crisis, said the failure to build enough homes "has led to record numbers of households, including thousands of families with children, being stuck in unsafe and unsuitable temporary accommodation".
"We’ve even heard of people having to heat up food on radiators," he added.
He welcomed the Government's commitment to increase the number of social and affordable homes but warned even more dramatic action was needed.
"The reality is that until we’re building 90,000 social homes every year, thousands of people, including families with young children, will continue to wake up in poor quality temporary accommodation," he said.
Of the total 6,724 social letting stock in Waverley, 5% were re-let in the last year.
The average weekly rent of these re-let homes was £135, equivalent to 45% of the average market rent in the area.
Dr Maya Singer Hobbs, senior research fellow at the IPPR, said: "Social homes must play a key role in the Government’s focus on housebuilding, for two reasons. The first is that there is no other way to meet the target of 300,000 homes per year.
"The last time that many homes were built in England was in the 1960s, when almost half were built by councils.
"The other reason is that there is a clear unmet need for social homes, with 1.3 million people currently on social home waiting lists.
"Building social homes can also help address other Government priorities, such as reducing child poverty by driving down housing costs."
Some 310 homes in Waverley were social rentals, where rent is based on a national formula that accounts for relative local earnings, and 102 were affordable rent, where the rent can be no more than 80% of the market value for the property.
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A Government spokesperson said: "We have inherited the worst housing crisis in living memory because of a failure over many years to build enough social homes, and the Government is clear that the only way to meet the demand for social homes is to build more of them.
"That is why we are already taking decisive action to deliver the biggest increase in affordable and social housebuilding in a generation and tackle one of the biggest drivers of homelessness by ending no fault evictions."