Reeves's Idiom doesn't contain tunes, but the Wm Chorley version is given with tune in Sharp Karpeles Vol2 p411. However Reeves does give another version from Sharp's manuscripts which I don't think is published elsewhere. This is from Music Book 4934, contributed by Miss Priscilla Wyatt Edgell who had it from an old man of 85 in 1923.

I would guess the Watersons got the Chorley version from my set of EFDSS Journals which at that time were held by their Hull folk club.

It is very difficult to date ceremonial songs of this sort and I wouldn't like to hazard a guess as to which of the two songs was the earliest. It is very likely that they both derive from an earlier song, possibly the French versions mentioned earlier.

I'm not a sight reader but the tune given in Sharp/Karpeles appears to be the one used by the Watersons.