I wouldn't have thought the police would not look into this matter. If it is a public street, then parking across a driveway is a bookable offence? It is my belief that you cannot park over a driveway on a public street even if it is your own driveway.
Not having access to a driveway means that emergency services do not have access. You should write to council and emphasise this fact. Should there be a fire, heart attack, act of violence, how would the appropriate people attend if the driveway is blocked?
I would write to council and point this out, ask them to paint “No Parking at any time” outside the driveway or some other obvious notice. Should there be a serious event on these premises (whose owners pay rates to council for services which I would think includes access to their homes from the street) and emergency services not be able to attend due to no action taken on this parking problem then you would have proof that you tried to bring this matter to someones attention.