The Day When That Round Car Hit Me Citroen C3

This brings up whether all cyclists should be required to have some sort of insurance? If we want to be acknowledged as legitimate road users wouldn't this be a responsible step?

No way.

I ride a bike to be free from all that crap.

You will find that in fact a lot of cyclists have insurance, e.g. through LCC, CTC, or BC membership, but also because a lot of people take out insurance because they want to be insured ... It's a driver myth that a lot of cyclists are not insured. In fact, in London it is known that many drivers are uninsured.

As cyclists cause very few collisions (95% or so (I think--I'd have to look up the exact figure--are caused by users of motor vehicles), providing third party insurance to members of cycling organisations is quite affordable and prevents creation of an onerous responsibility on cyclists to take out their own insurance individually. It would make for a real disincentive to cycling if that were the case.

Given the many other membership benefits you get with membership of a cycling organisation, it is certainly worth becoming a member. Being an LCC member, I'm of course biased towards recommending that London cyclists become LCC members, but the CTC and BC are also excellent organisations to be members of, also several of them--I'm a member of both LCC and CTC, for instance. The more cyclists become members, the better these organisations can work for the common good.