Looked into Michael KIlgarriff, "Sing Us One of the Old Songs,' Oxford 1998.
He lists Repertoires of the Artistes, Lyricists and Composers, Index of Song and Sketch Titles, and a Date-list. List of song publishers. Core Song List. Covers 1860-1920.

Joybell, you may have seen this book already. It is big, with 848 pages, but, as Kilgarreff states, by no means is it intended to be complete. "Significance" and "Popularity" are two of the criteria.
I looked for Dodger songs, and only found these, but line-by-line check for possible equivalent titles could turn up some:

Sam Cowell- The Artful Dodger. The Dodger's Return. (Dicken's based)
No listing for the "We're all Dodgers" type of song.
Charles Sloman (also see Cowell) Artful Dodger

Sir George Robey- I'm Dodging It. (?)

Funny Little Thomas (Joseph)- We Are All Humbugs. This may be a "We're all Dodgers" song.

Harold Montague- The Artful Coon (may belong to the Artful Dodger group).

J. L. Toole- No Dodger songs listed. 'The Grasp of an Honest Hand'?

No "Cheat" songs but they must be there.