It does not seem to be a private road. I didn't see any
notices to that effect, and none of the drivers of the
goods trucks seemed indignant that I was using the road.

Access to the road is from the A41. If you're driving towards
Aylesbury from Bicester you come first to the point where
the old railway crossed the road on a overhead bridge. The
bricks of the retaining wall are still in place. A few yards further,
there is a left turn into a small industrial estate. Taking that left
turn, so you are moving parallel with the alignment of the old
route, you take another left turn which bears right onto the
old track bed.