One week after the FCA successfully brought a test case against eight insurers over their denial of business interruption claims, it said customers who renewed home or motor insurance policies should pay no more than new clients using the same sales channel.
"The FCA estimates that its proposals will save consumers 3.7 billion pounds ($4.74 billion) over 10 years," FCA interim chief executive Christopher Woolard said.
The regulator singled out "price walking", or complex pricing practices that allow insurers to raise prices for consumers who renew their car and home insurance policies year after year.
The Association of British Insurers said insurers and brokers had begun tackling the problem, but Sheldon Mills, the FCA's interim executive director of strategy and competition, said they had not gone far enough.
"This is a radical change we are putting forward today," he told a media briefing.
The FCA said it had identified 6 million policyholders paying high or very high margins in 2018, who could have saved 1.2 billion pounds collectively.
The proposals are being put out to public consultation until January, with final rules published next year.
Shares in motor and home insurers Admiral, RSA and Direct Line fell 2-5.6%.
Insurers were due by Tuesday to tell smaller business customers the implications of last week's ruling that some of them were wrong to reject tens of thousands of claims from firms battered by the COVID-19 pandemic.
But some said they only received an email from their brokers, telling them their insurer was likely to send a "holding" letter saying it needed time to decide on next steps.
The FCA has told insurers to make interim payments wherever possible on policies where the legal process is complete or the claim has been accepted in full or in part.
The regulator and some insurers are still considering whether to appeal the judgment, which the FCA said found in favour of policyholders on the majority of key issues.
Lloyd's of London [SOLYD.UL] syndicate Arch said on its website that the judgment was likely to be appealed. RSA said its position on outstanding claims would not change while appeals were being considered.
($1 = 0.7812 pounds)
By Huw Jones and Carolyn Cohn