Who owns the milestone?

Milestones are (usually) the property of the Highway Authority, which is your County Council or Unitary Authority. They may have delegated the maintenance to a Highway Contractor. In the case of trunk roads, the delegation will be to Highways England and then to their Highway Contractor. You need someone’s permission if you want to work on a milestone by the wayside. If it’s on private land, you need to get the permission of the land-owner.