An effective solution would be to change D&D procedure and make their intial response to a Training Fix call to be "Roger triangulation in process please state your position". In the case of a genuine Training Fix being required the student, PPL or instructor would respond "Position approx 2 miles North of Gloucester". D&D would then confirm that "your fix position indicated 4 miles North North West of Gloucester".
That's plenty enough uncertainty to get you into serious trouble given that ...
Old-fashioned 'lost procedure' is increasingly becoming irrelevant in south central and south east UK due to the airspace complexity.
The only time I've ever reported "uncertain of position" (
not on 121.5) I knew where I was to within three or four miles, but I also knew that controlled airspace was not very far away.