Comcover is the Commonwealth insurance fund, which operates much like many large corporations, ie there is an element of self insurance, which is in reality much like a massive excess, but over and above that there are commercial insurers lurking in the background, largely via Lloyds agencies I believe.
Comcover Insurance & Risk Management - Department of Finance and Deregulation will tell you everything you might want to know and more - that is if you're really short of bedtime reading.