Anyone renewing their home or motor insurance should pay no more than they would as a new customer, under a proposed shake-up of the sector.
The Financial Conduct Authority (FCA) said the "radical" reforms would save consumers £3.7bn over 10 years.
If adopted, the plans would see customers, old and new, buying on the same channel getting the same price.
So those buying, for example, online would get the equivalent deal, whether renewing or a new customer.
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 FCA has been studying ways to prevent six million people paying on average £200 too much on premiums.
Overall, the FCA had suggested consumers were overpaying by £1.2bn a year.
How price rises affect you
So-called price walking is when a customer is charged more, year after year, by staying with the same insurance company - even though their risk is no greater.
The FCA points to an example in which a new customer for home insurance typically pays £130 for a year's cover.
But for the same policy, having stayed with the same insurer for five years, that annual premium rises to £238.
For motor insurance, new customers pay £285 while customers who have been with their provider for more than five years pay £370, according to the FCA's example.
The FCA has been looking to tackle the loyalty penalty - a result in the growth, and encouragement, of shopping around for insurance, overdrafts and utilities.
Those who switch get the best deals as new customers. Those who stay loyal get charged more.
Ten million policies across home and motor insurance are held by people who have been with their provider for five years or more.
This is accentuated by the poverty premium - you get a worse deal if your finances are less "resilient", you struggle with handling money, or do not have internet access to find the cheapest deals.
The regulator's research into household and motor insurance had already found that more than one in 10 people were paying very high prices for their cover. One in three of them were vulnerable in some way, perhaps elderly or lower paid.
It said that some insurers targeted price increases at those less likely to switch.
However, the FCA also found that those switching very regularly are likely to be flagged by insurers, and possibly blocked from the best deals.
So, somebody considered to be a savvy shopper by looking around would also be penalised.
Under the proposals, firms would be free to set prices for new customers, but they would be prevented from gradually increasing the renewal price to consumers over time, other than in line with changes in a customer's risk.
Firms would also need to consider how they offered fair value to all customers over the longer term and were being told to report certain data to the FCA, so that it could check the rules are being followed.
The proposals will now go to consultation until late January, and could come into force during next year.
Dame Gillian Guy, chief executive of Citizens Advice, called for swift implementation of the plan.
"It is nearly two years since we submitted a super-complaint on the loyalty penalty and we're pleased to see the FCA is proposing strong action to crack down on this systematic scam," she said.
The Association of British Insurers (ABI), which represents the sector, said there were winners and losers under the current system.
"Insurers and brokers have already begun to tackle the issue of excessive price differences between new and existing customers through an industry initiative that has seen over 8.5 million pricing interventions across home and motor insurance worth £641m," said ABI director general Huw Evans.
"It is vital that price comparison websites and insurance brokers are subject to the same level of supervision and monitoring by the FCA to ensure a balanced approach."
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