The Sunday Times understands that the issue was raised with HMRC in August, but the authority failed to alert the Department of Work and Pensions (DWP) until October.
A spokesman said: “We apologise to those affected by this calculation error and are working to fix the issue, although the impact is small with the difference in tax owed being around £5 in most cases.”
It is understood that HMRC hopes to solve the problem this summer.
However, critics have called for HMRC to reveal how long it has been going on for, how many pensioners have been affected and to actively issue them with refunds.
Sir Mel Stride, the shadow chancellor, said: “If HMRC have been charging millions of pensioners too much tax then questions need to be answered and the matter must be urgently put right. Ministers need to ascertain what has happened and what action is being taken to ensure these sorts of errors do not happen again.”