Martin Lewis has urged people to make a claim as around 100,000 are entitled to up to £6,000.
Speaking on his ITV Martin Lewis Money Show Live on Tuesday evening the consumer champion urged people to act now. He said: "Make sure you look this up if it smells like it is relevant to you or someone you know. There are hundreds of thousands due an average of £6,000 back in underpaid state pensions because of a former DWP error."
Martin added: "Married women and widows may have been underpaid. It's complicated."
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The money manager explained more about the situation as he said: "If the old state pension, so those ages 70 or above roughly, was less than 60% of their husband's, first of all there's some automatic top ups and backdating and they're working through it now so you'll get them.
"If your husband was 65 after March 16 2008 and the wife's pension didn't rise when he retired and it's under 60% you may get that top up. There's also an automatic top up for any woman aged 80+ who was paid under £85 per week on the state pension.
"But going back to the big theme, the old state pension under 60%, you will need to claim it. There are free tools online and you can call the pension service to chat."
Martin went on to advise that some claims can be backdated by up to a year even if the woman has since died. He said: "It's way too complicated to spend too long on so go and do your reading if you may be in this category.
"Basically, if you're a woman aged over 70 and you got a very low state pension then you need to go and do some reading on this."
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