Just looked on arial images of BK and there's a clearing at the end of the woods next to the barrow, you basically arrive at this point after following the woodland path up.
This is where I'd seen evidence of camping and you'd never be spotted there. I park where the road has woods on both sides and turns quite sharply near Humblebee Cottages, the path in the woods starts here too.
I think that'd be a superb place to do a solo camp, very atmospheric and secluded with the woods then onto Avebury for the solstice.
The perfect combination, I'm jealous!