Sounds like a music hall song to me. I wonder who the songwriter was. Here's a recording of Bob Keightley singing it:
http://sounds.bl.uk/World-and-traditional-music/Bob-Davenport-Archive/025M-C1047X0042XX-0400V0

My transcription:

HE USED TO SONG IN HIS SLEEP
Songwriter: ???
[as sung by Bob Keightley]

He used to sing in his sleep
All night long.
In the middle of a beautiful dream,
You would hear him start to scream:
"Alice, where art thou,
Alice, I want you for my own."
His wife's name was Mary,
So now he's sleeping alone.



Gee, I wish the song were longer....