An investigation has established that one insurer gave the incorrect amount of money to 3,000 customers over the course of several decades. Four in 10 of the Friends Life customers whose policies were reviewed, or 1,200 people, were paid too little and will receive compensation.
At least one other firm is understood to have been affected by similar problems with annuities, the irreversible contracts that turn a pension pot into a lifetime income.
The shortfalls were caused by computer malfunctions or human error when calculating the total amount the customers had saved in their pensions. The savers affected were routinely given too little money to invest in an annuity, leaving them short of income.
Most are aged over 60 and have had no way of establishing whether their payments were too small. Some pensioners have died after suffering losses that may never be recovered by their families.
The disclosures come as regulators prepare to order insurance companies to review thousands of annuities issued since 2008 over fears of mis-selling.
The Financial Conduct Authority is understood to be finalising the questions that will be sent to customers.
Hundreds of thousands of people are feared have been sold annuities that failed to reflect their health. Most were in the dark over their right to shop around for a better deal.
Experts said the mis-selling inquiry could show the miscalculations made by Friends Life were "the tip of an iceberg", although a spokesman for the FCA said it would not force firms to carry out checks.
Ros Altmann, the government's adviser on older people, said:
"Savers trusted that the income they were offered was fair.
"Now we know that not only were they often mis-sold policies, but some firms couldn't even calculate the right numbers to make sure people got the right payments."
The admissions add weight to calls for those locked into annuities to be given a second chance at getting a fair deal.
Around five million pensioners who had already bought an annuity will be excluded from the pension freedoms that take effect in April.
The Telegraph disclosed in November that Aviva, Britain's largest insurer, was paying compensation after discovering that staff sold inappropriate deals to hundreds of customers.
Friends Life is embarking on a similar process of issuing repayments. Its calculation errors were discovered in a routine system "spot check", a spokesman said. An old computer program had incorrectly calculated the final bonuses that were paid to some savers. The spokesman insisted that the issue was isolated to just one group of customers who held so-called with-profits pensions with Winterthur Life, a company Friends Life acquired in 2011. However, the spokesman was unsure whether other firms used the same software.
Its investigations also found evidence that human error had "compounded the problems", with staff making mistakes when inputting data into computers.
Aviva is in the process of buying Friends Life and acknowledged the scale of the problem in document issued to its shareholders this week.
"While comprehensive controls are in place, there is a risk of error in the calculation of the prices of [unit-linked] funds due to human error in data entry, IT-related issues and other causes," it said.
"Additionally, it is possible that policy charges which are deducted from these contracts are taken incorrectly, or the methodology is subsequently challenged by policyholders or regulators and changed retrospectively. Any of these could give rise to compensation payments to customers."
David Smith, director of financial advisers Tilney Bestinvest, said:
"We see insurance companies making errors of this type every few months, with clients getting a lump sum of money, albeit usually a small amount.
"The public doesn't have a chance of judging whether their payments are accurate."
A spokesman for Friends Life said: "Were wholeheartedly apologetic to all of the customers affected and will be putting them right as well as ensuring this issue isn't repeated."
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