All i can do is reiterate my answer which is fact.
I'm an underwriter for UKI, we underwrite tesco, egg, direct line, privilege, churchill, natwest, prudential....etc.
With ourselves the car DOES NOT have to be insured elsewhere, this obviously proves that it's NOT a requirment by law for it to be insured.
We do have a stipulation that it doesn't cover you to drive vehicles within your household, this stopping people driving numerous cars whilst only insuring one.
If you still have any doubts i suggest you contact your insurer.