Affected pensioners will receive a letter outlining any changes to payments
An estimated 95,000 public sector pensioners have been overpaid £126m since 1978, the Cabinet Office says.
About 5% of civil servants, teachers, NHS workers, judicial and armed forces personnel have been overpaid by an average of about £1,300 each in total.
The money will not have to be repaid but many face pension cuts.
The Scottish government says it will not cut the pensions of former council, fire and police staff in Scotland, even if they were overpaid.
SNP work and pensions spokesman John Mason said they wanted to avoid pension cuts but the UK Treasury had refused consent to amend pension regulations for 6,000 retired teachers and NHS staff in Scotland.
They, and retired armed services, judicial staff and civil servants in Scotland will see their pensions cut.
Mr Mason said the Treasury "must reconsider" adding: "It's time for common sense to prevail. No pensioner should have to suffer for this bureaucratic bungle."
Letters are being sent to pensioners across the UK explaining what has happened.
But the Royal British Legion said the letters were "non specific" so people did not yet know what their new pension payments would be.
Shadow chief secretary to the Treasury, Philip Hammond, said: "It is completely unacceptable for the government just to tell pensioners they have been affected but refuse to give them the full facts until January.
"95,000 people will now face a Christmas of uncertainty and fear, wondering what is going to happen to their pensions."
The overpayments began in 1978 and were caused by an "incorrect indexation" of pensions.
In a written statement to MPs, Cabinet Office minister Liam Byrne promised a National Audit Office investigation but said there was "no single cause".
A spokesman for the Cabinet Office would not calculate how much people would lose, as it would vary widely between individuals and pension schemes.
But the Scottish government said it believed the average annual overpayment to Scottish pensioners in the NHS scheme had been £161, while for those in the teachers' scheme it was £384.
Mr Byrne said some pensioners would have their payments reduced while others would get below-inflation increases.
Asked about the situation at his monthly press conference, Conservative leader David Cameron said: "You have to ask why this was allowed to go on for such a long time.
"This government has been in power for a lot of years. They have to get a better grip."
Liberal Democrat Treasury spokesman Vince Cable, who first raised the issue in the Commons, said the figures highlighted "decades of incompetence".
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"The government must not claw back any money from the workers affected," he said.
"Pensioners should not have to pay the price for government error."
He said if people faced "big reductions" to pensions they should be staggered.
Xafinity Paymaster, the firm named in the Commons on Monday as having made overpayments, said in a statement it was "not at fault".
In a statement, it said: "A number of public sector pension scheme administrators, including Xafinity Paymaster, were not notified of the correct GMP data," the company said.
"The result is that some public sector pensions have been overpaid."
It said it was "working very closely" with its public sector clients to help identify problems and "correct future pension payments as quickly as possible".
Mervyn Kohler, of Help the Aged, said he was pleased pensioners were not being asked to pay "for a mistake that wasn't theirs" and urged pensioners to check if they are entitled to benefits.
But Chris Simpkins, of the Royal British Legion, told the BBC he had seen one of the letters that had gone out and added: "There is not a hint of an apology or a recognition that people are going to be troubled by this. I find that quite unbelievable."
He said many people on low fixed incomes and facing high food and fuel costs would be very worried about getting a below-inflation increase and "in some cases therefore are going to see quite a significant reduction in their weekly income".
The £126m estimate does not include the separate NHS and teachers' schemes in Scotland and Northern Ireland and the separate civil service scheme in Northern Ireland.
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