McDonnell, 'Songs of Struggle and Protest', prints 'Tune: "My old friend John"' which I had read as the title of an older song unknown to me. But it could be read as an indication that then old tune has been written by a person Ernest Jones describes as "My old friend John" which at the first glance looks consistent with John Lowry mentioned above.
The tune given in 'Songs of Struggle and Protest' is of course completely different from the tune Martin Carthy sings.

Wolfgang