Mudlark, the words passed down to you orally (I assume) are amazingly close to the sheet music at the Levy site. There are only very minor differences.

THE ORGAN-GRINDER'S SERENADE
(Words and music by Chas. K. Harris. Arr. by Jos. Clauder. 1897)

Standing alone in the doorway, grinds the old hand organ man,
Turning that shiny old handle, playing the best that he can.
Not a soul stops or will listen. Quickly they all pass the door.
He heaves a sigh as they go by. They've heard those tunes before.
Yet close by the pavement stands a little miss.
"Here's a penny. Please sir, play me a tune for this."
Then the old man looks down at her: "Bless you, my sweet little maid.
If you will stay, don't run away, I'll play my serenade."

CHORUS: "After the ball is over," softly the organ did play.
"After the dancers leaving." "Please, mister, come every day!"
"Creep, baby, creep. Mamma will surely catch you.
Creep, baby, creep. Mamma is near to watch you."
"While the music is playing," was the next strain played.
Dear old sweet tunes that were heard morn and noon,
'Twas an old serenade.

Time passed, and still this wee maiden came to that spot every day.
Oh, how the old man's eyes glistened, and how that organ would play!
But one day he missed this angel. Poor man, his heart ached with pain.
"Why don't she come, my little one?" He waited, all in vain.
From a pretty cottage, just across the street,
There came forth a lady, face so sad and sweet.
"Baby is longing to see you. Come in, sir. Don't be afraid.
She's going to die. Please, sir, don't cry. Play her your serenade."

CHORUS: "After the ball is over," softly the organ did play.
"After the dancers leaving." "Please, mister, come every day!"
"Creep, baby, creep. Mamma will surely catch you.
Creep, baby, creep. Mamma is near to watch you."
"While the music is playing," was the next strain played.
Dear old sweet tunes softly played in that room.
'Twas her last serenade.