"While a large number of people shop around, many loyal customers are not getting a good deal. We believe this affects around 6 million consumers."
The regulator has raised concerns about how pricing leads to consumers who do not switch or negotiate with their provider paying high prices for their insurance.
The FCA estimates that around 6 million policyholders pay high prices and are not getting a good deal on their insurance, including 1 in 3 people who are potentially vulnerable.
Its research found that if those customers paid the average premium for their risk they could save around £1.2 billion a year.
In particular, the FCA found that insurers often sell policies at a discount to new customers and increase premiums when customers renew, targeting increases at those less likely to switch.
The FCA says it is now undertaking a "range of activities in order to address the problems" and will consider banning or restricting practices like raising prices for consumers who renew year-on-year or requiring firms to automatically move consumers to cheaper equivalent deals.
It is also considering banning practices that could discourage switching – including restricting the way that firms use automatic renewal.
The FCA is also considering whether firms should publish information about price differentials between their customers.
Christopher Woolard, executive director of strategy and competition at the FCA, said: "This market is not working well for all consumers. While a large number of people shop around, many loyal customers are not getting a good deal. We believe this affects around 6 million consumers.
"We have set out a package of potential remedies to ensure these markets are truly competitive and address the problems we have uncovered. We expect the industry to work with us as we do so."
Becky Downing, CEO of buzzvault home insurance, commented: “The pricing of home insurance is based on far too much ambiguity. In fact, contents insurance is a big black hole where insurers don’t really know what they are covering, so resort to blanket policies that don’t reflect what someone actually owns. 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. People need insurance that is in sync with their lifestyles and bespoke to them, ensuring they are not overpaying and simply covered for exactly what they own. Let’s hope this package of remedies kick-starts the move to better deals for consumers.”