Some 44,000 of those hit by the error are believed to have died before learning of the issue, with some underpaid by up to £128,000.

About 94,000 are believed to be still alive.

In total, an estimated £1bn of state pension payments due was not paid out, according to the National Audit Office report.

About 1 in 8 arrears payments is for £40,000 and an estimated 9 in 10 victims could be women.

Former pensions minister Steve Webb, now working for actuarial consultants LCP, says the underpayments have been going on for decades but action was only taken after a series of cases were brought to the attention of the DWP in early 2020 by his company in partnership with This is Money website.  

In May 2020, LCP published a paper entitled: ‘Are thousands of older women being short-changed on their state pension’, which was based on a Freedom of Information request submitted by Sir Steve in February 2020.  

Sir Steve says he believes around 90% of those affected are women.   

He said: “This report highlights the fact that DWP failed to act over a period of many years when errors were found in state pension assessments. Tens of thousands of married women, widows and the over 80s have been underpaid, with arrears in some cases exceeding £100,000.  

“It is very worrying that errors are still being made as part of the correction exercise, where the highest standards of quality control should be in force. DWP also needs to do everything it can to track down the families of pensioners who have sadly died and never received the pension they were due.  We now need full transparency from DWP about the correction process, with regular updates and a full explanation of exactly which cases are being reviewed. It should also explain how these errors were allowed to go on for so long and what lessons have been learned.”

The National Audit Office report suggest the errors were due to mistakes made by the Department for Work and Pensions in assessing pensions.

The government will now need to decide how best to pay compensation to those affected and potentially the families of the deceased.

Average compensation payments could be £8,900 each. The NAO report says the underpayments vary between as little as 1 penny up to £128,448.37, with some underpayments dating back to the mid-1980s.

Tom Selby, head of retirement policy at AJ Bell, said: “The fact pensioners, some of whom will have been struggling to make ends meet, have been underpaid state pensions to the tune of £1 billion is nothing short of a national scandal. 

“Tragically, of the 134,000 people underpaid by an average of £8,900 each, around 40,000 are estimated to have died before being compensated. Furthermore, those lucky enough to still be with us may have been living in penury when they should have been enjoying their retirement.

“The 94,000 people still alive who are owed money by the DWP need to get it back as soon as possible. They also deserve answers about how this was allowed to happen over such a long period of time.”

Mr Selby says the government must look how the mistakes happened and ensure they are avoided in future.