Insurers are in the Financial Conduct Authority's sights as it brings in new steps to stop consumers being penalised for loyalty to their motor insurers.
The finance and insurance regulator has been concerned that many insurance firms increase prices for existing customes each year at renewal - a practice known as price walking.
"This means that consumers have to shop around and switch every year to avoid paying higher prices for being loyal. It also distorts the way the market works for everyone," it said.
"Many firms offer below-cost prices to attract new customers. They also use sophisticated processes to target the best deals at customers who they think will not switch in the future and will therefore pay more."
The FCA's new rules will stop firms price walking from September 2020. Insurers will be required to offer renewing customers a price that is no higher than they would pay as a new customer.
The regulator added: "It is likely that firms will no longer offer unsustainably low-priced deals to some customers.
"However, the FCA estimates that these measures will save consumers £4.2 billion over 10 years, by removing the loyalty penalty and making the market work better."
From January 1, 2022, motor insurers will be required to report data to the FCA so it can supervise the market more effectively, and they must give most consumers easier methods of cancelling the automatic renewal of their policy.
The FCA will also review the effects of the remedies over the course of 2022, ahead of a full evaluation in early 2024.
"We are making the insurance market work better for millions of people. We will be watching closely to see how the market develops in the future and to ensure firms continue to deliver fairer value to consumers," said Sheldon Mills, executive director, consumers and competition at the FCA.