There are other threads on here which suggest that the use of the tune called Slane (Lord of all Hopefullness, Be Thou my Vision) as a hymn tune, predates its use for Banks of the Bann (which seems originally to have had a different tune). Hymnary.org says that it is the tune to "With My Love Come on the Road", in a collection by Patrick W. Joyce. However older than all of these are the Lakes of Shillin/Lakes of Coolfin/Willie Henry/Willie Leonard family of songs, and if you listen to Nic Jones singing The Lakes of Shillin then the melody is very similar.

We Plough the Fields and Scatter is German (Wir Pflugen) and attributed to Johann A.P. Schulz. I have just listened to Martin Carthy singing John Barleycorn on Youtube, and its completely different.