I haven't heard these progammes so I confess to arguing from a position of ignorance. However, I doubt it could be said that Lomax invented the radio ballad form. What he did pioneer was the intercutting of songs and actuality, as per Blues in the Mississippi Night, and this doubtless had a considerable impact on Parker and MacColl.

Even so, Parker always cited American documentary radio producer Norman Corwin as his major influence. In particular, Lonesome Train and Ballad For Americans.