(fixed link: click)

Looks like a list of songs from the show is:
- All That Gas
- A Ballad For Christmas
- Brother Men
- The English Way To Die
- Gallows Pole
- Geordie
- Hanging Johnny
- An Innocent Man Is Never Hanged
- Jack Ketch
- A Long Way From Home
- The Magic Number
- Sam Hall
- The Show's The Thing
- There's Gonna Be A Commission
- Upon Tyburn Tree

(via the US Catalog of Copyright Entries - link)

None of these songs really jump out to me as that song, but several are also fairly vague. As the person who suggested that this play may be where your song originated, I won't rule it out yet, but the list isn't exactly promising.