That would be Vaughan Williams rather than Baring Gould, "Monks Gate" being the place (near Horsham in Sussex) where that particular variant was collected, from Mrs. Verrall.  Published in the Journal of the Folk Song Society, as Bruce says above (vol. II, no.8, 1906, I think; the one Bruce mentioned is another variant).  So far as I remember, they only used the second 2 lines of that tune; the rest was mostly "Johnny I Hardly Knew You", with a bit of something else stuck in as well.

Though written music would make a helpful start, they played around with their sources so much in this that probably nobody could make an accurate transcription without having the recording to listen to, or a memory far more reliable than mine; I don't have a copy of "Rocket Cottage", as I'd ceased to take S. Span seriously by then (downhill from the day Carthy left, I reckon).  You go for it, and I'll think about it as well.