Arthur Shuttlewood records (in his imaginative ‘UFOs Over Warminster’ 1979) that “tradition has it that an early Saxon chieftain and his family were interred in the bald patch of earth on the top of the mound in the midst of tree growth” – neatly combining two common story themes – to ascribe prehistoric barrows to Saxons, and the idea that vegetation will not grow on certain graves.
I know Copheap / Cop Heap very well, and have some photos of the place dating back to the '80s. It has its own atmosphere, and fab views. Yes, the very top is bare-earthed. Let's hope no more digging occurs there.
(Liked your 'imaginative' pun on A. Shuttlewood's book. Having read it a few times, and enjoyed it, I'm still none the wiser. As he himself stated, he was a journalist, so you'd expect some skepticism from him...)