Universal Credit, introduced in 2011, was first rolled out to simplify the benefits system and to incentivise paid work.
It combined six means-tested social security payments into one lump sum. But the policy has been heavily criticised with people waiting more than five weeks for money.
The new system also means the housing benefit section of Universal Credit is now not paid directly to the council.
Figures published by council bosses show 4,116 people across Doncaster are now on Universal Credit.
It is estimated that 7,500 Doncaster tenants will be rolled out over the next four years.
But of the 4,116 on the new system, documents show 3,134 or 76 per cent are in rent arrears.
Data shows nearly a third of all Universal Credit cases have an Alternative Payment Arrangement for direct payment to St Leger Homes.
Nigel Feirn, head of finance and business assurance at St. Leger Homes, said: “We continue to work collaboratively with the Department for Work and Pensions and Doncaster Council to ensure all customers are supported to make and maintain their Universal Credit claim.
“Referrals to our Tenancy Sustainability Service for intensive support continue to grow from commencement in 2018, and we have supported 2,602 customers and secured in total over £854k of financial gains for supported clients.”
"Financial gains have been as a result of support with benefit claims or appeals, applying for grants, and accessing financial support to reduce debt."
Council bosses say there now are around 35 new Universal Credit claimants per week over the period to date, but there have been times where new claimants have been around the ‘50 per week level’.
Doncaster Council is owed around £1.38 million in rent payments.
Bosses add that rent arrears from the 4,000 plus claimants under the previous system stood at around £900,000 and say the impact of Universal Credit on arrears has increased by nearly £500,000.
The percentage of people on Universal Credit in rent arrears has decreased. In November 2018, there were 2,304 UC claimants, of which 1,840 or 80 per cent of tenants owe rent.