Thanks, Malcolm. The song in "Mary Barton" is certainly the Four-Loom Weaver. It begins (as quoted in the novel):

Oi'm a poor cotton-weyver, as mony a one knoowas,
Oi've nowt for t'yeat, an oi've woorn eawt my clooas
Yo'ad hardly gi' tuppence for aw as oi've on
My clogs are boath brosten, and stuckins oi've none
Yo'd think it wur hard,
To be browt into the warld,
To be-clemmed, an do th' best as yo con.

There are another six verses given. I do apologise for confusing the two songs. I was partly led astray by the fact that on my old Topic LP "The iron muse" Bert Lloyd sang this song as "The poor cotton weaver", whereas the recent Topic CD of the same title has Harry Boardman singing "The Hand-Loom Weaver's Lament". I didn't spend time listening to Harry Boardman's song and just assumed it was the same one. Whoops! That should stop me sticking my nose in.
Best wishes, Matthew.