The city regulator carried out a market study into the pricing of home and motor insurance, and found competition is not working well for all consumers in these markets.

The FCA is concerned that pricing in these markets leads to consumers who don’t switch or negotiate with their provider paying high prices for their insurance.

The FCA estimates that around 6 million policyholders pay high prices and are not getting a good deal on their insurance – and could save a combined £1.2bn a year if they paid average premium prices.

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 6 million consumers.”

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. It said that most firms, when setting a price, include their expectations of whether a customer will switch or pay an increased price.

As a result of the study, the FCA is considering banning or restricting practices like raising prices for consumers who renew year on year, or requiring firms to automatically move consumers to cheaper equivalent deals.

The regulator is also looking to stop practices that could discourage switching – including restricting the way that firms use automatic renewal.

Salman Haqqi, personal finance expert at money.co.uk, said: “The FCA’s findings that six million insurance policyholders are getting a bad deal for their insurance is unfortunately not surprising to anyone who has seen their premiums go up every year.

“The FCA also found evidence that some firms are doing their best to stop customers from shopping around and switching provider. We welcome the news that the FCA is reviewing the auto-renewal process to stop those firms that abuse their customers’ trust this way.

Nigel Pocklington, chief commercial officer at MoneySupermarket, said: “The FCA rightly highlights that ‘consumers who switch or negotiate their premium can get a good deal’. Insurance is a sector where loyalty, or disengagement, has never paid. Whether on car or home insurance, you can bring your premiums down substantially by shopping around and not accepting the price on your renewal notice. It takes a few minutes online and the benefits far outweigh the so-called hassle.”