Whatever the origin … this skipping rhyme has been around for decades… maybe for over a Century or more. Ding Dong Bell comes from 1580! The Manchester Ship Canal was completed in the late 1800s. The Titanic sank in 1912… so when did this rhyme first appear?
Most nursery rhymes have their origins back in history, some as far back as and many we used to sing/ chant are horrible, some involving killing, but we still chanted them as they were cemented in tradition and we really didn’t think about what they said/ meant!
I used to sing the Alley AlleyO in the 1940s in Gloucester … others talk about it being from the North or in London, or all over the UK … there are a lot of suggestions as to what it means or where it came from, obviously a lot were formed in different locations and related to the local naval events going on at the time.
Basically none of this is ‘false’… it’s all suppositions that have grown into local ‘folk-lore’. As a child you believe what you are told… the answer is NO ONE knows… until someone spots it in an old book or some archive perhaps?