Using public transport isn't always about whether people can afford to own a car, it is also about convenience. Many railway station car parks and park & ride car parks prior to lockdown were often full during Mon to Fri. These are people that already own a car but still made use of public transport. At the moment convenience is not the biggest priority for most people, they are putting health and safety first. Roads are getting busier by the week, even though some lockdown measures are still in place. Boris's recent return to work message will only increase traffic from where it is now.
Also most insurance companies don't only offer car insurance. They also do travel insurance, health insurance, business insurance etc. It may be a case of having to pass some losses in certain areas of their business onto others. Have a look at the share price graphs for most of the major insurance companies and see how much of a gift the last four months has actually been.
Also, I dare say insurance companies look at more than just the last three-four month period when they review their car insurance portfolio and set their premium rates. I seem to remember that certain parts of the UK have been badly affected by some quite extreme weather (heavy rain and flooding) during the last 12 months. There’ll have been lots of cars irreparably damaged by flood water that will have been automatically written off. Incidents such as this could actually mean insurance companies see an increase in their claims costs for the last 12 months compared to previous years, even in spite of less ‘road activity’ because of the lockdown.
On lockdown specifically, although there should have been fewer accident related claims because people will have been driving their cars less during lockdown, the frequency of some types of claims may have actually increased - malicious damage claims (cars being keyed and dented while parked up and not being used). The incidence of theft claims might also have been on the increase during lockdown as some less honest sectors of the community fall on hard times and look for a quick and easy way to ‘earn’ a dishonest pound or two

; they may see car theft might as one such way they achieve this.
I’m not defending the insurance industry, nor do I have an affiliation with any insurance company. I also hate it when my premium increases for no apparent reason. Just saying that there will be a number of factors that could affect why premiums increase. It always pays to shop around at renewal, and never ever let your insurance auto-renew as there’s likely to be another insurance company out there offering a better price.