I have checked my references. The article, by Ian Russell(who knows everything there is to be known about the play) is in the EFDSS, Folk Music Journal, 1979 edition(vol 3 no 5). And while it has twenty-odd versions of the song, not one of them has precisely the Waterson tune(though they all have similarities).So we'll have to wait for someone else to come in with the precise sourcee of the Watersons' version. Now, I'd guess they got it from Bert Lloyd, I believe that is how he sang it.
   If you've never heard an old New Orleans band(not a modern trad band) doing "Didnt he Ramble", find one! I was amazed when it dawned on me that what I was hearing was an old Derbyshire tune re-formed into this classic bit of New Orleans folklore. I used it(The Derby Ram) as a processional brass tune with Welfare State International theatre company, in a winter processional show in Wath-on-Dearne, when I was a callow youth.