It seems most likely the Ally Ally O- comes from the Irish nursery tune, and brought to the NW with the huge Irish diaspora, and adapted. It is logged in the Irish Musical archive from Dublin,.
The famous Clancy Brothers notably sang this song as the " The Big Ship sails on the "Illy Ally Oh" - rather than Ally Ally Oh. The Salford ship canal did not open until 1894- but had a large Irish community working on the docks canals etc, so it would have been well known.
The Irish Traditional Music Archive certainly list it as "Illy Ally Oh".
https://www.itma.ie/dustybluebells/explore/round-and-round-up-and-down-out-and-in-1/big-ship-sailed-to-the-illy-ally-oh
It is also listed as an 1880 tune, here
https://www.songfacts.com/facts/traditional/the-big-ship-sails.
So it is a long time before, the opening of the ship canal that it was being sung.
Certainly was part of the link to the sea and the communities around the docks. and chimes with children and playground songs- so popular in the past.
So originally a nursery rhyme - added to and extended in folk spirit- and probably perhaps with opening of the Manchester ship canal and largeIrish communities in Salford and Manchester, who knew the nursery rhyme already. And popularised later.
It travelled well across the playgrounds of the land- but mainly NW, I believe. Beautifully represented , in the Taste of Honey film with Rita Tushingham and Thora Hird- about her life and expecting a baby with a black Liverpool sailor.
The SS Arctic which left Liverpool and collided with another ship off Newfoundland- in 1859 may be the best candidate in terms of a ship going don - it was the biggest loss of life at sea in the Atlantic on a steamer before the Titanic. No women or children survived at all. 359 lives were lost. It sank on the 27th September, perhaps late in the day Though many ships over the years wuld have sank on this date, it seems the most prominent, and a big incident only later eclipsed in popular memory by the Titanic.
It was shocking news both sides of the Atlantic. according to Wikipedia-New York New first heard of the disaster on October 11, with the arrival of the survivors rescued by Lebanon. Later that day, Baalham's report, telegraphed from Halifax, was received at the Collins Ship offices.
https://en.wikipedia.org/wiki/SS_Arctic_disaster
So news travelled slow in those times. but a close fit. To an added rhyme to the ditty. Though a lot of ships went down, and it may be simpler origin.
rhttps://www.thoughtco.com/the-sinking-of-the-steamship-arctic-1774002
The Bromley is listed in a web chat as leaving Salford quays and sinkinking in the Irish Sea on the last day of September, but I could not find an internet record of this, in this quick search- it is not memorable in news terms - so it chimes more with the arctic- but perhaps it is just a simple rhyme after all that fits people in different places.
An Intriguing little mystery
Best
Richard Scott, Liverpool
I will ask next time I go in Merseyside Maritime Museum what they think.