No, the council does not have to have insurance against negligence. Then again, just because they don't have insurance does not preclude you from taking action against them for negligence. It just means that, should you win, the damages would have to come from the council coffers, not their insurer.
To win with this, you are going to have to demonstrate negligence on the part of the council - presumably because they left an old tank in situ in the property that corroded through and leaked. You are probably best approaching the CAB to see if they can help you prepare a letter to make the case for your claim.