Around six million insurance policyholders are not getting a good deal, according to the City regulator.
The Financial Conduct Authority (FCA) made the comments as it published an interim report into the pricing of home and motor insurance.
If those customers paying high premiums paid the average price for their risk they could save around £1.2 billion a year, the regulator said.
It is considering remedies to improve competition, which could include banning or restricting practices such as raising prices for consumers who renew year on year or requiring firms to automatically move consumers to cheaper equivalent deals.
Other potential remedies under consideration include restricting the way that firms use automatic renewal, which could discourage switching.
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 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."
The regulator intends to publish a final report and consultation on remedies in the first quarter of 2020.
The FCA said it is concerned that consumers who do not switch or negotiate with their provider end up paying high prices for their insurance.
The watchdog 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.
- Longstanding customers pay more on average, but even some people who switch pay higher prices.
- From the FCA's consumer research, one in three consumers who paid high premiums showed at least one characteristic of vulnerability, such as having lower financial capability. For consumers who bought combined contents and building insurance, lower income consumers on below £30,000 pay higher margins than those with higher incomes.
- People who pay high premiums are less likely to understand insurance or the impact that renewing has on their premium.
The FCA said that most firms, when setting a price, include their expectations of whether a customer will switch or pay an increased price - but this is not made clear to the customer.
The regulator said it will also continue its work to ensure firms improve the oversight of their pricing practices.