Staff shortages at the Department for Work and Pensions have led to thousands of carers being overpaid benefits that they could be repaying for years, a report by the government’s spending watchdog has found.

In some cases, carers face repaying more than £20,000 they received in error, a task that could take 34 years, the National Audit Office (NAO) said.

In 2018-19, the Department for Work and Pensions (DWP) detected 93,000 overpayments of carer’s allowance, compared with an average of 41,000 a year in the previous five years. The NAO said the department was detecting “significantly more” overpayments because it had recently put in place more people and new systems.

While many overpayments were for just one week, some went on for more than a decade before they were discovered. At the end of March, 133 people owed more than £20,000.

Frank Field MP, chair of the work and pensions committee, said the report “devastatingly laid bare the incompetence at DWP, and its stark human cost”.

In November 2018, DWP had 104,000 unprocessed change in circumstances notifications. Photograph: Libby Welch / Alamy/Alamy

Carer’s allowance, now worth £66.15 a week, can be claimed by those who provide at least 35 hours of care to someone who receives a qualifying disability benefit.

But carers do not always realise that the sum they receive is linked to their earnings, and that if they take home more than £123 a week the allowance stops, or that studying more than 21 hours a week is a bar to claiming.

Carers have to give details of their earnings when they apply, but can be caught out when their circumstances change.

The NAO found that staff shortages meant that many people who had notified DWP about changing circumstances had not had their details processed.

In November 2018, the department had 104,000 unprocessed change in circumstances notifications. It said that these delays meant that overpayments had not been dealt with in a timely manner.

Overpayments are clawed back through lower benefits and deductions from earnings, and the NAO said that while on average it would take a carer just over three years to clear their debt, those owing £20,000 could be making repayments for the next 34 years.

The NAO’s investigation followed the Guardian’s revelation that a growing number of carers were facing fines and prosecutions as DWP sought to claw back overpayments.

Emily Holzhausen, director of policy and public affairs at Carers UK, said overpayments had caused a lot of stress.

“It is clear the DWP’s decisions about the handling of carer’s allowance have resulted in carers not being told about overpayments quickly enough and this must be urgently addressed,” she added.

A DWP spokesman said the report recognised the progress it had made in addressing overpayments. “We have introduced new technology to prevent overpayments and improve debt recovery. And we continue to make people fully aware of their responsibility to correctly report earnings and changes of circumstances.

“We have a duty to the taxpayer to recover money in cases of fraud or error but safeguards are in place to ensure deductions are reasonable.”

Field said: “There was already plenty wrong with the way we recognise carers’ invaluable contribution. Rather than making things worse, why doesn’t the department just spare us all: end this massive scandal, focus on the real fraudsters and write off the overpayments it has allowed to build up unchecked.”