The difference is for a car to be driving on the road, insurance is a legal requirement, to cycle it's not.
It is, IMHO, by and large a reflection of the risk. I can do a lot more damage with my car than I can with the bike, usually the bike (and rider) will come off worst (as in the OPs Case) and usually any damage to a vehicle, or other property will be relatively minor and much more affordable to pay. That is of course not tos say that a cyclist cannot cause a serious injury or indeed fatality.
The risk posed by a cyclist is much lower and thus, so are the premiums, its why third party insurance is a give away item with memberships of cycling groups. Looking at it a different way, my 3rd party cover via Cycle UK costs me £75 a year, it covers me, the missus and the kids for unlimited milage, i get a fee membership to an advocacy group, a few bi monthly mag, and access to discounts on goods that usually means the cost of the "insurance" is about £30 a year. Meanwhile, my car insurance is £265.
* it is important to remember that even though a person is not insured, that does not mean they are not liable. If you are hit by an uninsured driver (or rider) who is at fault, you can still claim against the individual - essentially via the small claims court, whether you see the money is a different matter - you cant get blood from a stone.
“If I had my way, I would write the word ‘insure’ over every door of every cottage and upon the blotting pad of every public man, because I am convinced that, for sacrifice that are conceivably small, families can be secured against catastrophes which otherwise would smash them forever.”
— W Churchill.
