This is from www.movinghere.org.uk about Irish migration to Liverpool in the 19th Century. It includes a line about seasonal workers returning to Ireland so it is possible Irish people took the song home with them:-
"Liverpool already had a substantial Irish population of about 50,000 in 1841, making it the most densely settled Irish town in mainland Britain.
It became the main pressure point for Famine refugees in 1847-1848. The historian David Fitzpatrick estimates that, at the height of the Great Famine, a quarter of a million passengers were arriving in Liverpool from Ireland every year. Of these, two-thirds departed overseas and many others were seasonal workers who later returned to Ireland."