S. Martin,
The car needs to be insured by yourself or somebody else before you can take advantage of your fully comprehensive cover (ability to drive another car with third party, fire and theft cover provided you have owner's permission) to drive that vehicle. The problem you will be facing is that you cannot tax a car if it doesn't have insurance for the duration of the tax period you are seeking to get, therefore you will be driving a car which does not have any road tax. You will also find that insurance companies may invalidate your claim if you happen to have an accident with the second car which is uninsured.
You should consider getting
temporary car insurance when you decide to drive the second car or get multi-car discount with your current insurer if you will be using it more often.
