I'm always bemused by these articles.
Some figures given a few years back by a BBC programme (don't still have details unfortunately) for the proportions of adult cyclists without 3rd party insurance showed that over 10 times that proportion of motorists, for whom it's compulsory, were uninsured! As commented above perhaps compulsion would mean insurance companies could charge us big premiums instead of next to nothing.
I agree with Dell, not having 3rd party insurance is insane. Same goes if you're a pedestrian, horse rider, or doing anything else that could affect someone else.
The reason insurance is so common is that most (but by no means all) household policies provide it, for all household members. Very useful it is too when one of your children rides their bike (in 1987) into the side of a brand new BMW M3 causing £250 worth of damage. The fact that the child is only 8 years old doesn't stop you from being liable.
My present household policy covers all of our bikes (but with a £100 excess for theft so only one covered for that!). That includes away from home anywhere in mainland UK. The 3rd party insurance part also definitely covers cycling. It's worth checking though. The previous one didn't cover away from home risks, apart from 3rd party, unless extra money went their way.
I also get 3rd party from CTC so who pays if I need it I don't know.