Uk regulators are to ban insurance companies from charging existing customers more than new ones for motor and home cover, in a move that could save policyholders 3.7bn over 10 years.

The financial conduct authority is trying to stamp out the so-called loyalty penalty the practice of increasing prices for existing customers every year so that the most loyal customers pay the most for their insurance.

The fca estimates that 6m people paid high or very high prices for their cover in 2018, and were overcharged by a total of 1.2bn.

The regulator has been consulting on solutions to the problem for almost a year and on tuesday unveiled proposals that would ensure existing customers were not charged more than new ones who bought through the same sales channel. for example, an existing customer renewing online would not be charged more than a new customer buying a policy online.

Fca interim chief executive chris woolard described the measures as the most radical shake-up of the general insurance industry in years and added that the proposals would save consumers hundreds of millions a year.

Shares in insurance companies direct line, admiral, sabre and aviva all fell in reaction to the news, while shares in price comparison site moneysupermarket were also down.

Under the new rules, insurers would be free to set prices for new customers, but they would be prevented from gradually increasing the renewal price to consumers over time a practice known as price walking. according to fca research, this results in new motor insurance customers paying an average annual premium of 285 while customers who have been with their provider for more than five years pay 370.

A ban on price walking is now proposed from the second half of 2021, the regulator said, and will be enforced by monitoring data from the insurance companies, as well as social media comments and feedback from customers

However, the fca has rowed back from one of the most controversial changes it proposed last year. the regulator had suggested a possible ban on automatic renewal of policies. the insurance industry said that banning automatic renewal would leave people at risk of being uninsured if they forget to renew.

On tuesday, the regulator said it would make it simpler to stop automatic renewal, but stopped short of an outright ban.

The association of british insurers said it would support the fcas work on insurance pricing. there are winners and losers in the way the market works currently, with those who switch insurance provider every year often ending up with lower prices, said huw evans, director-general of the abi. the fca has confirmed that insurers have not made excessive profits.

Consumer group which? welcomed the new rules and called on the regulator to check that insurers complied with them.

The fca must move swiftly to introduce these changes and closely monitor insurance firms to ensure they do right by their loyal customers, said the organisations head of money, gareth shaw. [the regulator must] show that it is ready to take strong action against insurers who game the system.

But industry consultants warned that people who normally shop around could be quoted higher premiums once new customer prices are equalised with renewal prices. mohammad khan, uk general insurance leader at pwc uk, said: for some young drivers who regularly shop around, their new annual insurance premium may rise by more than 50.

Michael sicsic, a former insurance regulator who now runs his own consultancy, said that the fca had taken the nuclear option, which would herald a complete overhaul in insurers business models.

What is quite different compared to previous interventions and policies is the measures they have taken to ensure firms dont avoid the intended outcome. for example, they will require a formal attestation of compliance each year. they havent done that before, he said.