The song I was thinking of is

The Weaver and the Factory Maid

which is in the Digital Tradition.

This is what A.L. Lloyd had to say (from a web site describing a cd - A.L.Lloyd - Traditional songs.

The weaver and the factory maid The earliest weavers' songs are from the time when handloom weavers went from village to village, setting up in farmhouse and cottage kitchens. Amorous chances were plenty. The invention of the powerloom and the establishment of textile factories brought a great change in the handloom weavers' lives. This song, lyrical and wry, curiously illuminates this moment in history when the handworkers were finding themselves obliged to follow the girls into the factories and weave by steam, and when country song was changing to town song. (12T86)

So I don't know if it is the song your after - possible one of many on similar themes.

Rana