In eight out of 10 cases in which people stuck with their existing pension provider to buy an annuity, the Financial Conduct Authority (FCA) found that they could have been better off financially had they shopped around.
It stated around three-fifths of people stuck with their provider, but on average the benefit of switching equates to someone having saved an extra £1500 into their pension before they retired.
The FCA, which launched an inquiry into annuities last year, said its findings paint a picture of such a "disorderly market" that it now plans to conduct a competition market study, which will include an investigation of annuity sales by pension providers to their existing customers.
The regulator will look for any signs that sales techniques designed to hang on to customers involve putting them off shopping around. If it uncovers any poor practice, it will ask firms to make immediate changes.
Annuities are a one-off purchase that people make when they retire, which converts their pension savings pot into a fixed annual income for the rest of their lives. An array of different 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.
Data analysed by the FCA covered around four-fifths of the 420,000 annuity sales that took place in 2012. Standard annuitants with no medical conditions had an average pension pot of £17,000 and enhanced annuitants had a typical fund of £26,800.
It estimates that 80% of those purchasing an annuity from their existing pension provider would benefit from shopping around and switching. For standard annuities, around 79% of people could get a better deal on the open market. Ros Altmann, an independent expert and former Downing Street adviser, said: "The reason why immediate action is so important is that this market affects so many people and the transactions they are making are irreversible.
"More than 1000 people every week are buying annuities and the market is worth £14 billion each year."