What I take to be the first publication of this song can be seen in Notes to the People by Ernest Charles Jones (London: J. Pavey, 1851), page 953.

The title is THE SONG OF THE LOW.

The only indication of a tune is the phrase "To a popular melody."

It has 5 verses that are identical to those posted above, plus the following chorus:

We're low—we're low—we're very very low,
As low as low can be;
The rich are high—for we make them so—-
And a miserable lot are we!
And a miserable lot are we! are we!
A miserable lot are we!