Realistically, the only times such insurance would be useful is where a cyclist is injured in an accident caused by themselves, a pedestrian, or another cyclist, or where a cyclist causes an accident for which they are liable. However, an accident not involving a motor vehicle is unlikely to cause more than minor harm, and the risk of a cyclist causing someone else damage is relatively slender and the type of damage is also likely to be minor.
Now I am not saying that such insurance would never be useful - indeed, there are rare instances when having the insurance would pay off. However, my view is that encouraging cyclists to get accident insurance has the undesirable consequences of reinforcing the belief that cycling is dangerous and may discourage people from cycling. Perhaps I am being cynical, but I can't help thinking that if more cyclists had insurance, it would be a natural progression for the ABI to lobby the Government to make cycle insurance a legal obligation. I am sure I am not the only cyclist who would meet this with strong opposition.