I phoned Nympsfield today because I am looking for a landing site near Stroud. Although they appear in the Lockyears Farm guide and quote a landing fee they do not allow powered aircraft in unless on gliding business apparently.
I don't know the specific position at Nympsfield, but you may well find that planning permission is a dominant factor. If the planning permission for a club was granted based on it being a gliding club, then it would be no surprise that non-gliding activities are precluded.