The FCA launched a probe into annuities last year and said it revealed such a "disorderly market" that it will carry out a competition market study looking at sales of annuities by pension providers to their existing customers.
The regulator will look for signs that companies try to hang on to customers by putting them off shopping around for a better deal.
If it finds examples of bad practice, it will ask firms to make immediate changes.
The FCA looked at around four-fifths of the 420,000 annuity sales that took place in 2012.
It found that 60% of people stayed with their current pension provider, but four-fifths of them would have benefited from shopping around and switching.
Those buying a standard annuity could have boosted their annual income by as much as £200 by shopping around and by £67 on average, the data showed.
Buyers of enhanced annuities could have been £290 better off or increased their annual income by £135, the FCA found.
Annuities are a one-off purchase that people make when they retire, which convert their pension savings pot into a fixed annual income for the rest of their lives.
A variety of annuity types exist, including standard ones that most people tend to get and enhanced annuities, where people in ill health, such as smokers, can get higher payments.
The FCA's report is due to be published in the next 12 months but campaigners are calling for action to be taken now.
Independent expert and former
"More than 1,000 people every week are buying annuities and the market is worth £14bn each year."
The FCA said firms generally expect annuities sold to existing pension customers to be more profitable than business on the open market.
"This makes taking effective action to ensure that people get value for money from annuities all the more important, and the new FCA review is a welcome and crucial step, as part of the Government's ongoing work on the issue."
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