Elizabeth and Mark, there's no need to go elsewhere, the "Moving on song" (along with most of MacColl's songs from the radio ballads) is in the DT here. To find the others, and songs recorded by MacColl, search the DT (search box in the upper right corner of the screen) for MacColl.
The song you asked for specifically is from the radio ballad "The Travelling people", as Elizabeth says, about the Romanies in England. The Radio ballads series, produced by Charles Parker in conjunction with Ewan and Peggy Seeger. There was also a discussion on the radio ballads late last year, and Ewan's work and influence is frequently discussed. Try a forum search for MacColl.
One small request, please try not to ascribe a song to a nationality, it is arguable that in folk song there is no such thing. If you are trying to provide more information, "..recorded by the Patagonian group 'Magillicudy Reeks'." is helpful; saying it is a Patagonian song because they recorded it is not, and it annoys the hell out of some of us!
Pete M