Gee Jack, I haven't heard the term 'first fittin' in absolutely years.

The words are pretty much the same as your own with differences mainly in the verse about the Royal Carriage. As Uncle Jim used to sing it, that verse ran:
                                                            
Well one day the Royal Train drew in an' I was fu' o' pride!                                          
I keeked intae the Royal Saloon and who d'ye think I spied?,                                                
I saw His Majesty, King George the Fifth, the Queen was by his side                                          
So I yelled wi' all my micht "Ye've got tae change for"

Change for . . . . .
                     Chorus

Wasn't sure I have recalled the word "keeked" correctly. I seem to remember hearing it used as referring to "Having a sneaky look / peeking"

Any ideas here.

Sorry, realised AFTER I posted my reply earlier that you had already stated that you didn't know the chords for the songs by "The Big Yin"