But those who regularly shop around for a cheaper deal, who are often younger customers, could end up paying more – with discounts potentially becoming smaller. “Price walking” – commonly known as the loyalty penalty – is a practice where existing customers are increasingly charged more the longer they stay with the same insurer. This has distorted the market as new customers may have been offered below-cost prices by firms to attract them in and then ended up paying more over time if they renewed their insurance.

The Financial Conduct Authority – which is introducing the new measures – found that millions of customers were being unfairly charged higher prices, including an extra £1.2billion in 2018 alone.

Martin Lewis, founder of website moneysaving-expert.com, has warned: “My best guess is firms won’t just cut renewal prices to match those for newbies, rates will meet nearer the middle. This will mean savings from switching will likely relatively reduce.”

He suggested checking at least two comparison websites; comparing these deals to Direct Line and other deals that comparison websites do not include; seeing if a multi-car policy would be cheaper and checking cashback websites.

Those struggling to find cover may want to check the British Insurance Brokers’ Association’s website at insurance.biba.org.uk/find-insurance.

Ryan Fulthorpe, at comparison website GoCompare, said: “It’s still important to shop around.”