Nancy of London/Yarmouth appears on The Critics Group sea album, 'As We Were a-Sailing' sung by Ewan MacColl, released by Argo records in the mid-1960s
John, like other members of the Group, added it to their repertoires
The song, with it's remarkable tune, was originally got from a singer recorded by H D H Hammond who described it as follows:

18   Nancy Of Yarmouth
H. E. D. Hammond, who collected this beautiful song, has said that it is "widely known in Dorsetshire on account, I suppose, of its fine tunes, since I have never come across a complete and intelligible set of the words".
Ewan MacColl (Peggy Seeger: Concertina)

I'm pretty sure a similar version was recorded by the BBC in the 1950s
Jim Carroll