The DigiTrad tune is clearly a variant, but, no, it isn't quite MacColl's tune. It may have been altered by "oral tradition" since it began making the rounds in the '50s or '60s.

The tune MacColl sings on "Matching Songs" is that attributed in "The Singing Island" to Mark Anderson.

Except for barely audible differences, that is also the tune Coppard used.