Just to add my bit to this, being born in, and spending the first 30-something years of my life in the Manchester/Stockport area I too remember this rhyme.

I've not previously heard of a connection between the Ship Canal and the song, and sadly I find that the Canal was officially opened on 21 May 1894.

The rhyme I remember accompanied a dance-game as described above, usually a girls game. I remember a chorus as well, though after all this time it could just be my mind playing tricks :)

The big ship sails through the alley-alley-o
The alley-alley-o, the alley-alley-o;
The big ship sails through the alley-alley-o
On the last day of September.

Ch:
Alley-alley-o, alley-alley-o;
The big ship sails away
OH!
The big ship sails through the alley-alley-o
On the last day of September.

AndyG