I'm reviving this thread just to mention that I listened today to the second of Morpurgo's Folk Journeys, during which one of the contributors made the same comment as C Stuart Cook above: that working four looms came in with automatic power looms. He suggested that the remake of the Poor Cotton Weaver version of the song to the Four Loom Weaver version dates from around the 1860s during the cotton famine.

That would be long before Becket Whitehead got hold of it, but it doesn't resolve whether MacColl was responsible for the present tune.