The Financial Conduct Authority (FCA) said it was concerned that some pricing policies harmed consumers, particularly the vulnerable.
It said it has already found some firms were not complying with rules about the information customers should receive when renewing their policies.
The FCA has written to CEOs of insurers saying it expects them to treat all customers fairly, whether they are new or long-standing.
Last month Citizens Advice called for an end to practices resulting in loyal customers being “ripped off”.
Andrew Bailey, the FCA chief executive, said: “Our initial work has identified a number of areas of potential consumer harm. We want to make sure that general insurance markets deliver competitive and fair prices for all consumers. 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.”
According to GoCompare, 65% of drivers renewed their car cover with their existing insurer in the last 12 months and 38% said they did so out of loyalty to their insurer.
Georgie Frost, consumer advocate at GoCompare said: “We welcome any investigation into this area because clearly something isn’t right and people feel they are being ripped off. Clearer rules and regulations will be better for everyone because we can’t have a system where it is the most vulnerable that are the hardest hit.
“It’s well-known that loyalty doesn’t pay when it comes to insurance. Just a glance at the feedback we receive from our customers shows that you can save hundreds of pounds on a policy without compromising cover.
“It’s imperative that people keep shopping around and switching to avoid getting ripped off, but more also needs to be done to make it clearer how customers can switch.”