My understanding is that it's illegal to park across a dropped kerb (that's been properly installed with planning permission) whether there's a car on the drive or not. However, it's civil law and not criminal hence Dibble's reluctance to get involved.Not quite.
Legal drive with dropped kerb.
Nothing you can if the drive is empty and someone parks across it.
You call plod if your car is on the drive and blocked in as that is "obstruction".
I found tons of references but this one doesn't have pop-ups and irritating cookie permissions.