The thing is, car insurance has been completely sewn up by the insurance companies. They effectively pay out for your losses and sort it out amongst themselves as to who pays, and how much, covering their own arses first.
It's not just cyclists.. A friend of mine ended up in the middle of a 3 car crash in a car that was insured 3rd party by a foreign insurer (long story but the car is registered in Dubai and he was driving it in Scotland on the only insurance he could obtain).
The incident was purely the fault of the car following him, who punted him into the back of a car carrying a heavily pregnant woman, simply because he was not paying attention. Neither of the insurance companies would even talk to him about covering his losses. They were keen to talk to his insurer about seeing if they could fit him up for the woman's compensation, and dealing with the fact that they'd opened her car up like a tin can to get her out, however.

The car insurance business in this country has become a totally self-serving cartel which needs to be sorted out, IMHO.

Anyway, compulsory insurance for cyclists is too daft to even be talking about. Politically, the last thing that will ever happen in today's climate is such barriers to be erected in the way of a healthy and green means of transport.
Car insurance companies need to be obliged in some way to compensate third parties if their clients have been found at fault, IMHO, because you'll have the same problem claiming for anything unless you have a bottomless pit of legal cover to call on.