DHs car insurance has been going up every year for the past few years, he has max no claims (9+ years) and when we got our new car a couple of weeks ago they tried to put the insurance up by another £300! It was just ridiculous, good no claims and premiums of over £1,200 per year, have no idea why. He'd been with the RAC for 15 years too!
Went onto price comparison websites and most other companies would give the same cover for about £700 cheaper (not just one fly-by-night, can't trust them as far as you can throw them company, but big well-known insurance companies). RAC couldn't match it so we changed. Insurance companies can be a law unto themselves at times.
On the other hand, when he got his first car at about age 28 all the insurance companies were charging similar prices, about £1,500 a year. We had to suck it up at the time, but 16 years later we were not willing to accept an insurance quote that was creeping up towards his first quotes years ago. Not sure why you're being quoted so high after lower quotes a few months ago, it can get ridiculous.
(Our last car was only worth about £500 and we paid more than that for the one year's insurance we had the car for. Current car worth £6,000 and paying £450 for the insurance! Much better value.)
Car insurance can be ridiculous, but as we have to have it in this country if we drive a car we are a bit stuck and are at the mercy of the insurance companies sometimes.