No one has pointed out the other option.
If it's so expensive to insure with all your mods..... try for a quote with no mods, completely standard car. Then if that is affordable, take your mods off the car, run it as standard for a year until you get rid of your points or premiums reduce. Then put them back on.
Better than selling the car or putting it in the garage and not driving it.
You could also try a couple of other things when doing quotes. See if it's cheaper with a parent on your insurance, that way you (the "high risk" driver) won't be driving it as often. (This used to help with my premiums when I was about 20)
Try changing the place you keep the car. IE, some policies will allow you to have the car registered at another address (eg a parents house with better/safer postcode) but still keep it overnight at your own house.
If its been a couple of years since you got the points on your licence, definately give the DVLA a call to check whether any have come off.
I called them 6 months ago and found that my 3 points had already come off and would not appear on my licence when I got a new one sent to me (due to changing address).
Insurance is going up, people are having lots of accidents (lots of bad weather in the winter/etc) and as more people take the risk of driving without insurance, any accidents they have push up premiums for those who do pay their insurance.
My insurance went up this year, even though nothing had changed in my circumstance, except no longer having points on my licence. Go figure.
Its a fact of life than sometimes stuff gets unaffordable. When I moved to London 7 years ago, I had to give up my GTI because I couldn't afford to keep running it. I sold it, bought a dirty cheap Polo and ran that until I could afford something better.
Hope you can avoid selling. As I said, try looking at insuring a standard car without mods, at least you'll be able to keep driving your car (albeit without mods).