I actually wrote a blog post about this last year:
"Over the last few years there has been a large fluctuation in insurance costs for motor vehicles. During 2020 and 2021 there was a significant drop in premiums, attributed to the Covid-19 pandemic and lockdown. With more people working from home or isolating there were less vehicles on the road. Drivers reported reducing their annual mileage by 40% during 2020 and Police forces reported a 26% drop in the number of road accidents attended during the same period.
By January 2022 all lockdowns had been lifted and life (and driving habits) returned to normal. This coincided with the Financial Conduct Authority's (FCA) new rules to stop the habit of some insurers hiking up renewal prices for loyal customers.
Also by then insurers were heavily paying claims made by businesses that were unable to open during the earlier lockdowns and who had claimed for loss of earnings and business interruptions. Although this didn't directly effect motor insurance, the same companies that insure vehicles generally also insure businesses. The money lost from these claims had to be made up by increasing the costs of all policy types across the board.
By February 2022 the Russian/Ukrainian war had started, leading to Worldwide financial instability and shortages of resources. This directly effected repairers ability to obtain parts for repairs (leading to delayed repairs & increased courtesy/hire car costs) as well as a hike in the price of parts. By October 2022 insurers were reporting an average 50% increase in the costs of claims.
Additionally, the cost of second hand cars has increased dramatically due to the unavailability of new cars (largely due to the semiconductor chip shortage that has been going on since near the beginning of the pandemic), so where a vehicle is written off insurers are paying out more than usual to policyholders as the Market Value of second hand vehicles has also increased.
As a result of this it is expected that Motor Insurance premiums will continue to rise over the next few years."
So long story short, massive increases in claim costs/payouts has forced the industry to increase premiums by an average of 30%. This has also led to many insurers pulling out of the market (for example Zurich are not providing car insurance after the end of this month) leading to a reduced pool of insurers willing to quote.