From what I can google, emigration of cotton spinners started before the Crimean War and continued some time after it. From Glasgow, the peak might have been the late 1830s.

In the second to last line, you'd have to sing um-be-rell-as to make it scan right, but I guess Ford or his source couldn't bring himself to write the local pronunciation down. But - how many working class people had umbrellas that far back, still less unemployed cotton spinners? I suspect that version is a later rewrite.