The way in which home and car insurance policies are priced is to be studied by the Financial Conduct Authority.
The regulator said it would look at scale of any harm to consumers from pricing practices, whom it affects and, if required, what actions should be taken to improve the market.
It has written to the chief executives of firms to set out that it expects them to treat customers fairly.
Citizens Advice has already warned loyal customers are being “ripped off”.
Andrew Bailey, chief executive of the FCA, said: “This market study will help us examine the outcomes from general insurance pricing practices and inform how, if necessary, we should intervene to improve the market.
“If change is needed to make the market work well for consumers, we will consider all possible remedies to achieve this.”
The FCA said it had already found some firms were not complying with its rules about information that customers should receive when they renew their policies and could use its regulatory powers against those with whom it had concerns.
In the letter to the heads of insurance firms, Mr Bailey said: “There is a significant risk of consumer harm if your firm has not implemented an appropriate pricing strategy with effective governance and controls to determine and monitor your pricing activities and evaluate how your pricing decisions will affect consumer outcomes.”
The FCA said UK insurers generated £78bn in premiums from customers and that 82% of adults had one or more general insurance product.