The Government announced a one-off payment in March for every home between council tax bands A and D, to help people cope with spiralling bills.
Despite a social media plea urging those who have not had the rebate to come forward, around a quarter of people in the city entitled to the £150 have not made contact.
The issue was raised at a council audit committee meeting by Labour councillor Paul Truswell, who said he had had "quite a lot of people contacting me about significant delays" in receiving the grant.
The council’s chief financial officer, Victoria Bradshaw, said in response that everyone entitled to the £150 would eventually receive it in some form.
She said: “We’ve got around 80,000 people who haven’t applied and who are eligible.
“We did do a social media [post] to try to encourage people to apply. And today, 24 June, is the last day to apply for that payment.
“We’ll then write a report confirming who’s had the payment against who hasn’t.
“[For those who haven’t], we’ll then credit their council tax accounts with £150 and then we’ll re-issue their council tax bills.”
Ms Bradshaw said that some applications for the grant had been flagged up as potentially fraudulent, which required extra checks.
She explained that council staff had had to work extra shifts and well over their normal working hours to process the money.
Although the Government did give the council extra funding to help with administration costs, the task required existing staff already familiar with the systems in place, she said.
Ms Bradshaw added: “On some applications, we’ve been able to make the BACS payment because we’ve confirmed that the person on the application form does pay council tax.
“We had others who we’ve issued Post Office vouchers for, because we couldn’t confirm the bank details weren’t fraudulent.
“The team that are dealing with this have gone over and above their normal work and they’ve worked extremely hard to get this resolved as soon as possible.”
The council had to apologise last month after it emerged some residents in the city had been paid the rebate twice over.