Prudential has begun a review of all non-advised annuity sales to existing pension customers since 2008, following a request from the Financial Conduct Authority.
The review will examine whether customers were given enough information about the advantages of enhanced annuities over standard annuities, and of shopping around.
The firm stated the review could result in "redress" for some customers.
In a message to customers on its website, the company stated: "Prudential UK & Europe wishes to advise its customers that it has agreed with the Financial Conduct Authority to review annuities sold without advice after 1 July 2008 to its contract-based defined contribution pension customers.
It stated the review would "examine whether these customers were given sufficient information about the availability of, and their potential eligibility for, enhanced annuities".
"The review will also look at whether these customers could have potentially received a higher income from Prudential or another provider. In due course Prudential will contact customers who may not have been given sufficient information and will provide redress, where appropriate."
In its results today (24 July), fellow life office Standard Life also revealed it was setting aside £175m for a review of its own non-advised annuity sales practices, also at the request of the FCA.
The news came a day after the FCA released figures showing most people were not shopping around for either annuities or drawdown products, despite the high levels of media attention on the issue.
In the third quarter of 2016, 56 per cent of people buying drawdown products were using their existing pension provider.
Of those buying annuities, 58 per cent were using their existing provider.
However, more people were taking up valuable guaranteed annuity rates (Gars) than in previous quarters.
Prudential revealed this month that it was pulling out of the annuity market completely. Its existing pension customers would be given access to a "panel" of external annuity providers.