I'm rather lost with the proliferation of links to versions of this song, but I haven't spotted this one, which I first heard as a kid at a family-and-neighbours sing-round-the-piano gathering. I believe I've also heard it sung by two female voices in harmony. I assumed it was a classical parlour arrangement of the tune that RVW says was the other Phrygian tune for it in the notes to the Penguin book (it isn't Phrygian, neither is the Penguin tune):

  X:1
  T:The Trees They Grow So High
  M:6/8
  L:1/8
  Q:3/8=108
  K:EMin
  z3 |e3  e2e|d3  dcB|A2c B2A|E3
  E2F|G2G G2A|B2B BAG|A2B AGF|E3
  z3 |e3  e2e|d3  dcB|A2c B2A|E3
  E2F|G2A G2F|E3  D2D|E3- E3 |B3|]

Yes it does go that fast, to spinechilling effect, though you slow down a bit at the end of each verse.

Where's it from?