I am 100% sure that the title is "The Shamrock and the Thistle". It tells the story of Irishmen going to Glasgow at New Year for a true Scots Hogmany. I can vaguely remember the first couple of verses that I will try to relay here. (Apologies to anybody that does remember it properly.)

Well come on, you true born Glasgow boys, and listen to my song.
I come to speak of harmony. It won't detain you long.
I wrote this little tune for you and I'll play it on my whistle,
And I think the name I'll give to it is The Shamrock and the Thistle.

Well, aboard the Royal Ulster Man, we had a dram or twa.
As daylight broke, we all awoke and spied the Broomalaw.
We journeyed o'er and went ashore for whiskey, stout and beer,
And soon the word was going round: "The Irishmen are here."
....

Maybe this will inspire a memory in someone out there.

HTML line breaks added. --JoeClone, 14-Oct-02.