Hi Stephen,
I am really tempted to say you will be ok to do that, as like you say it is a private drive. But I am not sure if I am being totally honest. It is certainly not a silly question.
But here let me give you some advice, stay away from the car. Once you start it the temptation to drive will be excruciating. Your car will be marked too, if it is the one you were caught in. If an ANPR copper comes past and see's you in the drivers seat, how will you convince him you haven't just taken it for a spin. He won't know, and probably won't care either as he just bagged himself a Disqualified Driver caught at the wheel with the engine running. It could open a whole can of worms.
So my advice is Don't do it. Think of an alternative, e.g get a neighbour to do it, or get a neighbour insured and take it for a spin every now and then just to keep it ticking over. Most peoples insurances will alllow them to drive other vehicles anyway. I left my car sitting there for 8 months, then couldn't move the bloody thing!!
One thing they said almost certainly would happen, was that because I got my licence back early due to the course, that I would get stopped within 3 months of being back on the road because they think they have got a diqual driver you see. And guess what I Did get stopped too. Within 3 weeks. And I had, had a drink the night before. I nearly collapsed. I was ok and I knew I would be, but it didn't half put the frightners on me. But everything was legit.
So, my advice is get someone else to do it, to be on the safe side.
All the best,
TVI