But HMRC has admitted it does not know which pensioners are affected as the documents have been destroyed.
Sir Steve Webb, a partner at LCP, who has campaigned on this issue for more than a decade, raised concerns that people will miss out.
The former pensions minister said: “It is truly shocking that so many people have been underpaid because of errors on their National Insurance record for time at home with children.
“It is even worse that tens of thousands of people, mostly mothers, died without ever receiving the correct state pension.
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“It is vitally important that HMRC and the Department for Work and Pensions are open and transparent about this whole process and that every effort is made to track down all those who may be entitled.”
The DWP estimates errors on state pensions arising from a failure to record time at home with children on National Insurance records at around 210,000 cases.
Most are mothers who are now over state pension age and should have had Home Responsibilities Protection (HRP) recorded to boost their pension pot. It particularly affects those in receipt of Child Benefit before 2000.
Around 150,000 people are believed to still be alive and around 60,000 have died.
The department estimates it will reach about nine in 10 cases where the person underpaid is still alive and 75 percent where the person has died, around 187,000 people or their heirs in total.
It will be writing to those most likely affected and carrying out a publicity blitz.
But it means more than 20,000 mothers and carers or their heirs would have to proactively come forward to claim the underpayment.
Caroline Abrahams of Age UK said: “It is extremely concerning that so many women have missed out on part of their state pension due to administrative errors.
“This needs to be fixed as soon as possible as the women who have been underpaid for many years can ill afford to wait any longer, especially given the cost-of-living crisis.
“Eighteen months to send out letters seems insufficiently urgent so while we are pleased the DWP is acting they must be given the resources required – staff as well as funding – so they can identify and reach out to those affected as quickly as possible.
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“This situation is fast developing into a national scandal – no pensioner should go without their due.”
Jan Shortt, of the National Pensioners’ Convention, said: “We are grateful that the underpayment of pensions to women due to the lack of recording home responsibilities will be rectified.
“It is also necessary for those who are not sure if they are eligible for restitution to contact the DWP and have their records looked at. Older women will be the main individuals affected by this and they should be paid immediately.
“It may well be that an individual could have had a better quality of life if their pension had been paid at the appropriate rate. Things change in society and whilst we might understand the reasons for the lack of recording before 2000, we urge the DWP to make every effort to ensure deficiencies in record keeping are dealt with.”
A Government spokesman said: “We have identified and are correcting an issue related to the historical recording of Home Responsibilities Protection on the National Insurance records for people who first claimed Child Benefit before May 2000.
“Most records will be unaffected, and we have launched a new online tool to help people check whether they need to claim. HMRC will begin writing to those likely to be affected this autumn. Where errors do occur, we are committed to fixing them.”
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