I think cyclists will have insurance to protect themselves and not those they injure. Has anybody ever heard of a cyclist (casual or regular) ever stopping and giving their details.
I do think that as cyclists start to outnumber drivers in central London, it is probably not too onerous to ask that cyclists are required to carry or produce ID as motorists are required to do. I don't think cyclists help themselves by being seen as above the law.
Ultimately rather than having rational law which the cycling organizations should encorage, we will see some bad cyclists kill/seriously injure a few innocent pedestrians and see a massive backlash against their irresponsible conduct and it will affect all cyclists.