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About 200,000 women could be in line for payouts averaging £13,500 to top-up the underpayment of their state pension for up to two decades.
The Department for Work and Pensions (DWP) revealed details of the underpayments on Wednesday.
The errors focus on automatic cash increases for certain married women, widows and over-80s dating back to 1992 with "enhanced" pensions.
The DWP estimated the bill for tackling the shortfalls to be about £2.7bn.
The underpayment relates to the "old" state pension system - affecting those who reached pension age before 6 April 2016 - which had special provisions for married women.
Under these old rules, married women who had a poor pension in their own right could claim a 60% basic state pension based on their husband's record of contributions.
However, some of these pensions were not automatically increased when they should have been.
"The action we are taking now will correct the historical underpayments that have been made by successive governments, and anyone impacted will be contacted by us to ensure they receive all that they are owed," a spokesman for the DWP told the BBC.
A review will now take place to assess hundreds of thousands of cases, which could take many months to complete. It will include cases where the underpaid retiree has since passed away.
'Are you sitting down?'
Lynda and John Hallaway
Some pensioners have already made successful claims for repayments, including Lynda Hallaway, who lives near Hull.
After Mrs Hallaway, 74, and her husband John, 73, filled out claim forms, she received a call from the DWP. She was asked whether she was sitting down, before being told she was entitled to a payment of £9,000.
They spent the money on their children and grandchildren, and on a holiday, but she says she imagines others, possibly in much greater need than her, will still not have received their payments.
"A lot could have been done with the money a few years ago. So I felt it was a great shame that they could not have that money," she said.
The issue was highlighted last year after former pensions minister, Steve Webb, tabled a freedom of information inquiry that revealed a large number of women were being paid state pensions below the expected rate.
"The scale of these underpayments is truly shocking. Whilst it is good that the government is now planning to address this issue, the plan to do so over five years is simply not fast enough," Mr Webb said.
"It is also quite shocking that DWP plans to stop paying interest on these underpayments. If the government is going to fix these problems it needs to do so swiftly and fairly."
The DWP set up a special unit employing more than 100 civil servants to investigate the issue, and on Wednesday disclosed the full scale of the problem.
The scale of the underpayments came to light in the details of a report by fiscal watchdog the Office of Budget Responsibility (OBR) report which was published alongside the Budget.
Underpayments investigation
The Department of Work and Pensions first became aware of issues with underpayments in 2020 and took immediate action to investigate the extent of the problem, pensions minister Guy Opperman told the House of Commons in a written statement on Thursday.
"This is an issue that dates back many years across successive Governments," he added.
From August 2020 to January 2021 the DWP analysed millions of state pension records which helped identify cases requiring further investigation.
The DWP began a correction exercise on 11 January to examine each of the cases identified.
The cases fall into the following four groups:
• People who are married or in a civil partnership who reached state pension age before 6 April 2016 and may be entitled to a Category BL uplift based on their partner's National Insurance contributions.
• People whose spouse became entitled to a state pension following a change in the law in 2008. Some people should have had their basic state pension automatically reviewed and uplifted. Underpayments occurred in cases where this did not happen.
• People who have been widowed and their state pension was not uplifted to include amounts they are entitled to inherit from their late husband, wife or civil partner.
• People who have not been paid Category D state pension uplift as they should have been from age 80.
"Rectifying these cases is a priority for the department and we will do it as quickly as possible," said Mr Opperman.
