Very pleased to read that the driver is uninjured.
That road is not far from me, it is mostly straight N/S with some sections overhung with trees. There is a 60mph limit on most of it: although it runs through the New Forest it is fenced, so animals should not be a problem. So I think the Police analysis of driver error is probably correct. How could the driver make a major direction input sufficient to run off the road? My guess would be pulling out to overtake and swerving back in when realising an overtake wasn't an option. Early Aeros had no airbags, as the photo makes clear: Series 4s do!
Is it a write off? Possibly not, the O/S front wheel looks to be in the right place, the N/S isn't visible. If the two beams that run from the tub to the front suspension are not bent then it should be repairable.