Let's not get too bogged down.
First – the car must have a valid policy in its own right. It needs this to be driven (by anybody) on the road. If it doesn’t have one it cannot be driven or even kept on the road. If it is on the road at the moment and the earlier policy has lapsed because of the death of your uncle an offence has been committed. (Quite who would be prosecuted is a little unclear because the person responsible for it is no longer with us, but the offence is committed nonetheless). If it does not appear on the Motor Insurers’ Database (and you can check this at www.askmid.co.uk) it is liable to be seized by the police under S165 of the RTA. Unless you have informed the insurers it is unlikely the policy will have been lapsed (because they won’t know of your uncle’s death) and it may still appear on the database. However, in the event of an accident cover will be denied.
Second – it is unlikely your existing policy will cover you because it will probably state that any “other vehicle” you might drive has to be insured in its own right. Even if you are covered it will be for Third Party only. This means if you have an accident, damage to your uncle’s car will not be covered.
My own view is that, as part of your duty as executor, you should transfer ownership of the car to yourself, register it in your own name and then insure it in your own name before driving it anywhere.