There are more than 2,700 individuals and families waiting for council houses in the town, which is more than 25 per cent higher than Swindon Borough Council's social housing provision - it owns 10,440 homes.
Many are currently facing a longer wait because there are "more social houses being sold or demolished than built".
This has happened because to increase stock the council sometimes buys back a home it has previously sold under the Right to Buy scheme, which is costing the council hundreds of thousands of pounds.
While buying one back means more are available it uses money that could have been spent to develop more homes, meaning the wait for families goes on.
The chief executive of Swindon homelessness charity, Threshold, Ben Harman, warned: "With more social houses being sold or demolished than built, Swindon faces a severe shortage of genuinely affordable housing."
He added: "Nearly 1,000 people are now in temporary accommodation in Swindon, a 25 per cent increase in one year, often in poor and insecure conditions. Thousands more are at unofficially homeless or living in inadequate or unstable housing, with no certainty about where they can go next.
"Safe, affordable social housing would give people in Swindon a foundation to start overcoming their challenges, regaining their independence and belonging in their communities."
Big Issue magazine recently highlighted a property in Frobisher Drive, in Walcot, sold to its tenants for £30,000, with a huge discount of just over £100,000 in 2015.
Needing more homes to offer, the council brought it back in 2021 at the market price of £150,000 and then spent nearly £8,000 of repairs before offering it for rent.
It therefore "lost" nearly £130,000 on the deal.
On Thursday, November 27 the new Green Group in the council brought forward a motion about such rules called "yo-yo homes".
Group leader, Councillor Tom Butcher, said he'd like to see the government follow the example of Scotland and Wales and scrap the right to buy in England.
He said: "It just takes properties out of social housing, it reduces the number of council houses available, and it puts the profits into the hands of just a few ex-tenants."
Cllr Repi Begum, also a Green Group member, said that in her view the scheme certainly needs urgent and wide-ranging reform: "It isn't fair and it costs councils thousands of pounds, and it has been implemented very badly.
"There is a housing crisis and Right to Buy is funnelling money to just a few people and making it harder for others to find a home."
Cllr Begum cited another "yo-yo home" in Castleton Road, in Middleleaze, which she said was sold for £108,000 to its tenants and then bought back by the council for £240,000, again a net "loss" of more than 100,000.
Cllr Ian Edwards agreed with the need for wide-ranging reform and said: "If there was enough council housing and they were sold at market value and the money used to replace them, it might be fair, but the way it's done, everyone loses out."
The motion asked for details of the total number of council houses sold under Right To Buy, how many had been bought back by the council, and the difference in price.
It would have mandated the council to send this information to the government which is consulting on reforming the Right to Buy scheme.
That motion was supported by Green councillors and all but one Conservative councillor but Labours votes meant it was defeated.
The cabinet member for housing, Cllr Janine Howarth, defended changes already brought in by the Labour government.
She added: "There were five recommendations to tackle the issue of councils losing stock and yo-yo homes.
"Reduce discounts - done. From November 2024, Swindon's maximum discount has been £30,000, not £102,000.
"Allow councils to keep 100 per cent of receipts - done.
"Extend the time in which councils can spend the receipts - done. From 2027 that will go from five years to 10 years
"The length of time before you can buy has been extended, from five years to 10 years."
Cllr Howarth pointed out that if the house in Frobisher Drive had been sold under the new rules, the "loss" to the council would have been much less, as it would have been sold at £102,000 and bought back for £150,000.
Council tenants were given the right to buy their council home by the Conservative government in 1980, and since then at least 2.4 million homes have been sold and the total of council houses in the country is estimated to have dropped to two million in 2017 from 6.5m in 1979.
The Ministry of Housing, Communities and Local Government has said it acknowledges the need to reform the rules on tenants buying their council homes, and has launched a consultation on possible changes.
A spokesman said: "We want to ensure that council tenants who have lived in, and paid rent on, their social homes for many years can retain the opportunity to own their home.
"However, reform of Right to Buy is essential to better protect much-needed social housing stock, boost council capacity and build more social homes than we lose, supporting the government's commitment to deliver the biggest increase in social and affordable housebuilding in a generation."