The problem centres on the Pension Strategy Computer System, and its inability to accurately uprate an element of the State Pension called the Graduated Retirement Benefit.
The ageing computer system, which MPs have described as "not fit for purpose", was introduced in the 1980s.
It was due to be shut down in 2020, but has been kept going on a temporary basis.
In 2021, the National Audit Office found that problems with the system had separately led to 134,000 people who had claimed their state pension before April 2016 not receiving their full entitlement. The average underpayment was estimated at about £8,900.
This problem, which mainly affects widows, divorcees and women who rely on their husband's pension contributions for some of their pension entitlement, is expected to cost the government £1.05bn.
"It is worrying that the DWP's IT systems have not kept pace with the demands on them," said Labour MP Sir Stephen Timms, chairman of the Work and Pensions Select Committee.
"A great deal of money has been spent on the Universal Credit programme - which is a good system - but other benefits like the state pension are relying on ageing and creaking systems."
In a statement, the Department for Work and Pensions said the errors were "decades old" and that "successive governments have not corrected this".
"A decision was made in 2002 not to make changes or corrections given the system's complexity and minimal impact on individuals, until a new computer system was introduced. The Department is assessing the scale of this issue and investigating potential remedies," a spokesperson said.