May I suggest the EH run a species of ape over the unique and magnificent ancient monument?....
Known as 'homo sapiens', these lightweight, sometimes hairy mammals are unhoofed bipeds, their fleshy feet causing less footfall damage than hoofed ungulates whose feet cut the surface. Light fencing is easily breached by these intelligent creatures, so to confine them a sturdy high wire and electric fence is required. Generally they are summer visitors but occasional winter migrations can occur and as homo sapiens are a prone to 'flocking' the fence should be strong enough to repel unwanted individuals from neighbouring herds.
... Oh. They already do.
