Well Quinn due to the problems are probably having more oversight by accountants and regulators, than many other companies. They have obviously satisfied regulators that they are financially solvent. Who knows, there may be companies out there, who are operating in less financially stable way. Who would have predicted that RBS were in a financial mess, before the sh*t hit the fan in 2008.
So I would not worry about this too much. Even if they did go bust, the administrators would take steps to protect current creditors as much as they could, the regulators would stop them taking on new business, renewals would probably be stopped and they would decide what to do with current policies. I suppose the worst that could happen, is that if you paid the premium as a lump sum, you could have the policy cancelled and not get a full refund of the unused premium. If you were unlucky to have an outstanding claim, I would expect this to be met out of resources available, but you could suffer delays.
If you are a person who worries, shop around using this site and/or a local Insurance broker.