The underpayments resulted from years of failures at the Department for Work and Pensions (DWP) and ‘repeated human errors’.

Those affected are estimated to be owed an average of £8,900 each in state pension compensation – although the largest underpayment was £128,448. Only 94,000 of those affected are thought to still be alive.

The errors refer to married and divorced women, as well as those over 80 who were entitled to uplifts in their state pension.

Some women retiring under the basic state pension system were entitled to an automatic uplift in their state pension when their husbands reached age 65. In many cases this did not happen, and women had to actively claim it before the uplift was applied.

The true value of the underpayments will only become clear once the DWP has completed its review of all cases. Estimations suggest that about £339m of the cash is due to go to pensioners who should have benefited from their spouse’s or civil partner’s national insurance (NI) record.

About £568m of the money is owed to widows and widowers who should have inherited more state pension entitlement from their deceased partner. A further £146m is owed to pensioners who should have had an increase in their pension at their 80th birthday.

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 £1bn 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.

“Once compensation has been paid, the government needs to undertake a comprehensive review of its processes to ensure these mistakes are never repeated. Trust in pensions is fragile at the best of times and failures such as this will not help. Sadly, it will likely take years, if not decades, to rebuild the confidence lost as a result of this scandal.”

Helen Morrissey, senior pensions and retirement analyst at Hargreaves Lansdown, said: “There is an expectation that the state pension you receive is what you are entitled to but in this instance, this was clearly not the case. A combination of manual error and a complex system means thousands of women have missed out on payments that could have made a real difference to their standard of living in retirement.

“Many of these women had no idea that they were even entitled to a higher pension and so did not ask about it and while the DWP has begun making repayments it is likely going to take some time before all those affected have been identified. Anyone who believes they might be affected should contact the Department for Work and Pensions.”