The reality is, as Moss suggests, the difference between scheduling and actual prevention/policing of damage. The Ancient Monuments and Archaeological Areas Act 1979 (the primary legislation behind current scheduling) doesn't mention planting of trees. Section 2 and Schedule 1 cover "control of works", but there's nothing about planting or plants/trees at all. So it seems that unless planting a tree constitutes "works", it may not be prevented by the legislation.

The barrows around Avebury have been tree-covered for a long time and I doubt that 'new' trees are deliberately planted now (although no doubt some may self-seed).