I was lucky enough to pick up an old copy of the Joe Gordon Album (songbook) in a second-hand bookshop, so here's a list of the songs and attributions, some of which have been mentioned above. (Note spelling as in the book too!)
The whole book is copyright James S Kerr, Glasgow 1959
I realise they don't all fit the musichall remit.

The Wee Toon Clerk - Old Scots Ballad, arranged Joe Gordon
Bonnie Wee Jeannie McColl - traditional melody, words by Joe Gordon
Coulter's Candy - traditional melody, arranged Joe Gordon
Fitba' Crazy - traditional melody, words by Joe Gordon
The Brewer Laddie - traditional melody, arranged Joe Gordon
The Govan Billiard Hall - words and music by Roddy McMillan
The Whisky Song - traditional Gaelic air, words by Marietta McLeod
Twa Heids are Better than Yin - traditional melody, WORDS by Joe Gordon (see Malcolm Douglas post of 2004)
Gypsy Laddie - traditional, arranged Joe Gordon
The Hielan' Chorus - traditional melody, words by Joe Gordon
Dance Tae Yir Daddy - traditional Scottish song, arranged Joe Gordon. (Northumbrian too?!)
Johnnie Lad - traditional melody, arranged Joe Gordon
Three Men Went A-Hunting - traditional melody, words by Joe Gordon
Fair Annie of Lochroyan - traditional, arranged Joe Gordon