if you are not taxed it may take the authorities a while to notice so that could be seen as some sort of "grace" but it is not. You can still be prosecuted for being 1 day without VED though that is unlikely. You can tax a vehicle online using the main V5 or the green slip at any time, so no excuse.
I once had my tax disc nicked & reported it. The cops stopped someone who was using it - he said he bought it in a pub. I said "Shouldn't he have bought one at the post office?"
I doubt if the charged him.