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.”