Living 'darn sarth' I don't know the term, but having looked at this explanation it looks to me the same as an easement under England & Wales law.
http://www.andersonstrathern.co.uk/practice/ru ral/servitude_rights/
It is right of one landowner over another's piece of land. It is most commonly applied to a right of access over the land, a right to put pipes in the ground for water or sewage, a right to light - that sort of thing. From your description of the physical layout, the councils land is landlocked and can only be accessed over your land. If that is true, it is the council that would have the right of servitude over your land - not the other way around.
Under England & Wales law it is an entirely different legal principal that allows one to claim ownership of a parcel of land - the law of Adverse Possession. It is not linked in any way to easements.