It means that for existing consumers their renewal price would be no higher than the equivalent new-business price.
However, with firms being unable to charge renewing customers more than new customers in future under the plans, it could mean the disappearance of some ultra-cheap deals from the market.
The proposals, made by the Financial Conduct Authority (FCA), would apply through the same sales channel.
For example, if the customer bought the policy online, they would be charged the same price as a new customer buying online.
Firms would be free to set new-business prices, but they would be prevented from gradually increasing the renewal price to consumers over time – known as “price walking”, other than in line with changes in a customer’s risk. The regulator stopped short of banning auto-renewals, which could have potentially left some customers without cover.
The FCA did acknowledge that some new customers, who are currently on cheap deals, may see the prices they pay increase.
During a “virtual” press conference yesterday, Christopher Woolard, interim chief executive of the FCA, said: “For people who shop around, look for the best deal, there will be good deals out there in the market.
“But ... at the margins there will be some people who are getting unsustainably cheap offers, often possibly offers that are designed to get them to renew year-on-year and become far more profitable customers. And we expect those offers to not be part of the market in the future.”
Processes such as having to wait on the phone and the accessing of information can make it harder for people to cancel contracts than it was to sign up.
Mr Woolard said: “It should be as easy to be able to cancel a renewal as it is frankly to sign up to one. That’s probably a good rule of thumb.”
Ten million policies across home and motor insurance are held by people who have been with their provider for five years or more.
The FCA previously identified six million policyholders were paying high or very high margins in 2018.
And the body said it estimates its proposals will save consumers £3.7 billion over ten years overall.