Norman Buchan established a Ballads Club at my secondary school (Rutherglen Academy, near Glasgow/Scotland) in 1957 and gave us all a great grounding in good traditional music. When he then went into Parliament in 1964 a new young English teacher Ian Davison (now a prolific songwriter) took over the club and one of his pupils brought in "The Sands of the Shore"; Kathleen Mitchell told Ian that she had learned it from her granny, but although Ian did some research on it at that time he failed to identify it.
I was a member of the Ian Davison Group (typical name for the times!) and we sang it around quite a lot; another former pupil Mary Stewart sang it regularly about then in the Kilmarnock Folk Club -- which is where I believe that Heather Heywood probably first heard it. And Heather eventually recorded it....
Seems like a possible time line to me, but I'd be delighted to learn any more from anyone who knows better.

And we had it as " He's a stranger to me and so let it be" (although the vowels were more Scottish!).