The version played on the Youtube clip sounds to me like the version Butterworth collected from Mr. & Mrs. Cranstone, give or take a few tweaks. Go to Take 6 and search under Child 24, for this version and many others with an essentially similar shape, from the Hammonds and George Gardiner. This one isn't Dorian, though - plain old Ionian, I think. The other one Butterworth collected is Mixolydian, and the one from Vaughan Williams is a bit of a mix.

The first time I encountered this song was the version recorded by Tony Rose many years ago, which has always been the one against which I measure all the variants. His concertina accompaniment used nothing outside the standard three-chord trick.