Prices paid for home and motor insurance are changing due to new rules coming into effect on 1 January to protect loyal and vulnerable consumers.
Anyone renewing their policy will pay no more than they would as a new customer, under regulations set by the Financial Conduct Authority (FCA).
That means prices for those who switch regularly will go up, while long-standing customers will pay less.
The FCA said the move would save loyal customers £4.2bn over 10 years.
Brian Brown, consumer finance expert at market analysts Defaqto, said there was no sign of insurers leaving the market as a result, meaning customers still had plenty of choice of products.
What the policy is designed to tackle
The policy is designed to end cases of "price walking", which is when a customer is charged more year after year, by staying with the same insurance company - even though their risk is no greater.
When announcing its plans, the FCA pointed to an example in which a new customer for home insurance typically paid £130 for a year's cover.
But for the same policy, having stayed with the same insurer for five years, that annual premium rose to £238.
For motor insurance, new customers paid £285 while people who have been with their provider for more than five years paid £370, according to the FCA's example.
The new rules are being brought in by the FCA in the New Year following a super-complaint from Citizens Advice about the loyalty penalty.
Those who switched have received the best deals as new customers. Those who stayed loyal were charged more.
Around 10 million policies across home and motor insurance are held by people who have been with their provider for five years or more.
Matthew Upton, director of policy at Citizens Advice, said: "Rip-off renewal prices have seen consumers paying over the odds for far too long. No longer can you be exploited just for staying loyal."
He added that people tended to be at a disadvantage if they were older, on lower incomes, or unable to access the internet.
"We welcome the FCA's bold new rules on home and motor insurance. We now need to see urgent action to protect consumers in the other markets," he said.
How insurance premiums are set
People can still shop around for the best deals, and will need to consider whether the policy matches their requirements.
However, premiums charged to all renewing home and private motor insurance customers by their insurance provider cannot be greater than the price they would charge to an equivalent new customer for the equivalent policy.
Individual premiums can still be set at different levels depending on factors such as a customer's age, type of vehicle, driving record and history of claims.
James Dalton, from the Association of British Insurers, said: "While the FCA recognises that these changes could lead to price rises for some who shop around regularly, all customers should get fairer outcomes in the UK's competitive home and motor insurance markets."
In October, the FCA introduced new rules requiring insurers to look more closely at how they offer fair value for consumers.
It should also be made easier for consumers to cancel automatic policy renewals, and home and motor insurance firms must report more data to the regulator.