Insurers could be banned from charging loyal policy holders more than new customers for the same cover.
The changes proposed by the Financial Conduct Authority (FCA) would mean an existing policy holder's price to renew their cover would be no more than the equivalent quote for a new customer.
Analysis from the FCA revealed new customers pay £285 for motor insurance but their equivalent who has been with their provider for more than five years would pay £370 to renew.
The FCA previously identified six million policyholders were paying high or very high margins in 2018. The FCA estimates its proposals will save consumers £3.7 billion over 10 years and it will monitor their impact.
Christopher Woolard, interim chief executive of the FCA, said: "We are consulting on a radical package that would ensure firms cannot charge renewing customers more than new customers in future, and put an end to the very high prices paid by some long-standing customers.
"The package would also ensure that firms focus on providing fair value to all their customers.
"We welcome feedback on the proposals."
According to the FCA, 10 million home and motor insurance policies are held by loyal customers who have stuck with the same provider for at least five years.
The FCA is also consulting on other new measures to boost competition and deliver fair value to all insurance customers.
These include product governance rules requiring firms to consider how they offer fair value to all insurance customers over the longer term and requirements on firms to report certain data to the FCA, so that it can check the rules are being followed.
Firms use complex and opaque pricing practices that allow them to raise prices for consumers that renew with them year-on-year, the regulator said.
It is seeking views on its proposals by January 25 2021.
