Around 90,000 retirement annuity holders could be in line for compensation after the City watchdog found evidence of poor behaviour in the way the deals were sold.
The Financial Conduct Authority (FCA) has been probing non-advised sales of annuities - and raised concerns that the way these deals were sold could have caused some customers to buy a standard annuity when they could have been eligible for a product with a better rate.
Those receiving compensation may get around £120 to £240 per year and around 90,000 customers could be affected, the watchdog has estimated.
Annuities give pensioners the security of a fixed income, often for the rest of their life, but they have been controversial due to concerns about people failing to shop around to get the best deal for their needs.
There are different types of annuities and some enhanced deals will pay customers a better rate, for example if someone is in ill health and has a lower life expectancy.
The FCA reviewed non-advised sales of annuities made by pension providers to their customers between May 2008 and April 2015 and looked at the information provided to customers.
The review examined more than 1,200 non-advised sales at firms which between them account for around two-thirds of the annuity market.
The FCA emphasised it had found "no evidence" of an industry-wide or systemic failure to provide customers with sufficient information about enhanced annuities.
It said many firms provided clear and comprehensive information, with written communication tending to meet the standards required.
But the watchdog did have concerns about significant oral communications at a small number of firms, normally involving phone conversations.
It said this "was likely to have caused some customers to purchase a standard annuity when they may have been eligible for an enhanced product".
The FCA said areas of concern include call handlers being heavily reliant on scripts, customers not always being made aware that they could get a better income by shopping around and where firms did not sell enhanced annuities they did not always inform customers or mention enhanced annuities when speaking to them.
There were also concerns that call handlers underplayed the increased rates that people could get by shopping around.
The failings were of sufficient concern at a small number of firms that they are now being asked by the FCA to review all non-advised sales from July 2008 and, where appropriate, provide redress.
These firms, which have not been named by the FCA, are also being investigated by the watchdog's enforcement division to determine whether further action is necessary.
The FCA will also ask a small number of the largest firms not involved in the sample to ensure they do not have concerns about their non-advised annuity sales.
The pension freedoms launched in April 2015 mean people are no longer required to buy an annuity when they retire and instead they have a wider range of choices.
Megan Butler, director of supervision - investment, wholesale and specialist at the FCA, said: "Annuities play an important role in providing an income for retirement. It is important that consumers get the right information at the right time in order to make the right decision for their retirement.
"While we have found particularly poor behaviour at a small number of firms, there is no evidence that firms have systemically failed to provide customers with the information required by our rules.
"Firms, particularly those outside our sample, should look at the report we have published today and consider whether they can make improvements."
Tom McPhail, head of retirement policy at Hargreaves Lansdown, said: "If you are buying an annuity, and tens of thousands of pension investors still do every year, you absolutely must shop around.
"In a small number of cases, your existing pension provider may actually be able to offer you the best deal on the market but the chances are that they won't. Shopping around means getting a better deal every year for the rest of your life; you only have to do it once so it is worth taking the time to do it well."
Yvonne Braun, director of long-term savings and protection policy at the Association of British Insurers (ABI), said: "As the FCA points out, the information firms have given customers about enhanced annuities in the majority of cases has been timely, relevant and adequate and enabled customers to make informed decisions.
"The industry has been focused on improving people's experiences of making retirement choices in recent years and is working hard to ensure the freedom and choice reforms significantly improve customer engagement in pensions."