Your version of the tune's opening phrase starts with an upward leap, which is normal for minor-mode tunes in the British Isles. The distinctive version I was thinking of doesn't - it starts high and descends, which is often thought of as an archaic melodic shape. The two tunes are obviously related but I'd bet the purely descending one is older.

I wondered if there is any record of the tune being used for something else, maybe in a liturgical context.