If those customers paying high premiums paid the average premium for their risk they could save around £1.2bn a year.
The FCA has warned that some six million policyholders aren't getting a good deal on their general insurance policies.
The watchdog made the claim in itsinterim report on its market study into the pricing of home and motor insurance.
It said that competition is not working well for all consumers in these markets and has raised concerns about a lack of switching and negotiations which can lead to consumers paying over the odds.
And it estimates those customers paying high premiums could save around £1.2bn a year. This includes 1 in 3 people who are potentially vulnerable.
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 six 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."
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.
As such longstanding customers pay more on average, but even some people who switch pay higher prices.
It claims that most firms, when setting a price, include their expectations of whether a customer will switch or pay an increased price. This is not made clear to the customer.
Additionally it said that firms engage in a range of practices to raise barriers to switching.
As such the regulator isundertaking a range of activities in order to address the problems it has identified.
Through new rules introduced in 2017, the FCA has already improved transparency on renewal for general insurance policies which has delivered significant savings to customers.
The FCA said it will continue its work to ensure firms improve the oversight of their pricing practices and deliver the changes required following other recent policy changes.
It is considering the banning or restricting of practices like raising prices for consumers who renew year-on-year or possibly requiring firms to automatically move consumers to cheaper equivalent deals.
The FCA is also considering whether firms should publish information about price differentials between their customers.
It intends to publish a final report and consultation on remedies in Q1 2020.
