Thanks for all the replies folks. I think I will move the heap of turf
elsewhere. The area covered is only about 5 feet by 4 feet, and it's
about 3 feet high. It'll be a pain in the neck to move it (and it is
such a nicely built heap, too!) However the tree is very venerable,
and beautiful, and having seen all the answers I don't fancy taking the
risk; further it will prevent the "nosey neighbour" (who was only
trying to be kind) from pestering me in the future.

Cheers and thanks
John