There was another thread on this a while back - it was written by the Brothers Malone, a music-hall act who wrote various versions of it "The X-town Mashers" including Ashton, Oldham and Rochdale, as already mentioned by DtG. I assume the Irish version was derived from the same source - maybe the Brothers Malone toured Ireland (in fact from their name they were probably Irish anyway), or maybe someone took it over there and rewrote it for the local market?

The late great Harry Boardman recorded a version of the Ashton Mashers preceded with the original song called "We are the Brothers Malone" from which the Mashers song evolved.

It was also recorded by Fivepenny Piece and it's available on their latest EMI compilation CD. Their version says "Down Stamford Street" rather than "Back Preston Street" - I've never heard anyone sing the latter although it's in DT (Stamford Street is the main street in Ashton). The Oldham Tinkers recorded Rochdale Mashers, too.

If anyone knows of any other versions, or recordings, I'd be interested.