I am hoping to exchange contracts on a house which includes an unlicensed airstrip which has been used very infrequently (according to the current owners).
There is no such thing as an "unlicensed airstrip" in the context that you put forward - there is simply a piece of land on which one or more aircraft has/have landed on at some time/times in the past.
You have no responsibility to maintain this piece of land as an "airstrip" and nobody (but you) has any right to land an aircraft on it now or any time in the future. You are at liberty to leave it as it is, park agricultural machinery on it, plough it up or graze cattle on it. If someone decides to land on it without your permission and writes off their aircraft (and themselves/their passengers), that is entirely their problem. Indeed, if they take out one of your cows or a piece of scrap agricultural machinery in the process you may well profit financially from the episode.