The badgers. They do a lot more harm than tree roots. I've seen massive land slippage caused by decades of badger activity which basically took out about 60 - 80 feet of a hillside above the Water of Leith for a distance of hundreds of yards. These animals can excavate on a massive scale. There are many examples of Ancient Monuments being destroyed by burrowing animals here in Scotland. On the Gask Ridge, the Roman Signal Tower at Black Hill was completely destroyed, the fine embankments of the Roman Fort at Lyne are being tunnelled out at an alarming rate (I was there yesterday). There is a fair bit of damage to the ramparts of a few of the Clydesdale Hillforts too.
It should be about "active management" of sites which should involve regular inspections and active intervention where damage is being done. RCAHMS says
"Rabbits and other burrowing creatures can pose a major threat to earthwork monuments both for the damage they cause to underlying archaeology and for the erosion of ground surfaces. Where this is a problem it may be necessary to have them eliminated by means which involve no disturbance of ground
levels, unless the species involved has legal protection, as is the case with badgers. Where colonies of animals are to be removed it is essential both to get rid of the resident population, and to introduce an active management regime which prevents re-infestation by either the removed species or by other species. There may also be a need to install rabbit-proof fencing. For further information Historic Scotland’s Technical Advice Note on Burrowing Animals and Archaeology should be consulted."

It really shouldn't be too difficult - but there has to be the will to sort it.