Joe Hill's pro-union 1913 song is based on the tune of "There is Power in the Blood of the Lamb," a hymn written by Lewis E. Jones in 1899. There's a reference to the hymn in the third verse.

Would you have freedom from wage slavery,
Then join in the grand Industrial band;
Would you from mis'ry and hunger be free,
Then come! Do your share, like a man.

There is pow'r, there is pow'r
In a band of workingmen.
When they stand hand in hand,
That's a pow'r, that's a pow'r
That must rule in every land--
One Industrial Union Grand.
Would you have mansions of gold in the sky,
And live in a shack, way in the back?
Would you have wings up in heaven to fly,
And starve here with rags on your back?

If you've had "nuff" of "the blood of the lamb,"
Then join in the grand Industrial band;
If, for a change, you would have eggs and ham.
Then come! Do your share, like a man.

If you like sluggers to beat off your head,
Then don't organize, all unions despise,
If you want nothing before you are dead,
Shake hands with your boss and look wise.

Come, all ye workers, from every land,
Come join in the grand Industrial band.
Then we our share of this earth shall demand.
Come on! Do your share, like a man.
The song was published in Songs of the Workers: On the road, In the Jungles, And in the Shops, 8th Ed., AKA "The Little Red Songbook" (Cleveland: I.W.W. Publishing Bureau, 1914)

Billy Bragg probably took the name for his song in homage to Joe Hill, but the tune Bragg uses is George Root's 1862 "Battle Cry of Freedom," written for the Union army in the American Civil War. Confederate composers had their versions too, without the word "union" in the chorus. This can explain the sense of deja vu that Billy Bragg fans may feel while watching Ken Burns documentary, The Civil War, as Root's tune is on the soundtrack.