Oh, I agree, Guest Dave, the borrowing goes on in both directions. Some tunes that began as folk tunes were turned into hymns, e.g. by RVW in the English Hymnal. Some more examples from this:
Staines Morris: Soul of Jesus, make me whole.
Dives and Lazarus: I heard the voice of Jesus say.
The Bold Fisherman: I think when I read that sweet story of old.
and a number of others.

Similarly, but less often, what started as hymn tunes get appropriated as folk songs, as with that version of John Barleycorn.I'd like to see a bit more if this, as there are some great strong tunes out there, often with rousing choruses, that are at risk of being lost to the collective memory.

Marje