Around six million home and motor insurance customers pay high prices and are not getting a good deal in the UK, the Financial Conduct Authority (FCA) has uncovered.
Published today, the FCA's market study report also reveals that one in three overcharged insurance customers could be vulnerable people, such as those on low incomes.
Insurers often sell policies at a discount to new customers and raise premiums when it is time to renew, targeting increases at people that are less likely to switch.
If customers paying high premiums paid average prices instead, the researchers estimate that they could save a combined £1.2bn every year.
"This market is not working well for all customers," said the FCA's executive director of strategy and competition, Christopher Woolard.
"While a large number of people shop around, many loyal customers are not getting a good deal. We believe this affects around six million consumers."
For customers that buy combined contents and building insurance, those on incomes below £30,000 a year pay higher margins than people on greater salaries.
The study also found that customers who pay high premiums are less likely to understand insurance or the impact that renewing has on their premium.
Becky Downing, CEO of Buzzvault home insurance, said that insurers often resort to blanket policies for contents insurance because they don't really know what they are covering.
"This means that the likelihood of a customer overpaying is even higher, not to mention complicated and costly when they come to make a claim," she added.
The FCA said that firms engage in many practices to raise barriers to switching, and don't make it clear to customers that they could pay more at renewal when pricing policies.
The regulator is now considering a range of remedies, such as forcing insurance companies to automatically move customers to cheaper equivalent deals at renewal.
It could also stop practices that discourage switching, such as restricting the way that firms use automatic renewal.
"We have set out a package of potential remedies to ensure these markets are truly competitive and address the problems we have uncovered," Woolard said.
"We expect the industry to work with us as we do so."