Here's my transcription of the 1952 Kennedy recording of the McPeakes from Matthew's link (plus the short discussion). Interestingly he sings only the 2 verses.

Mick

---

MY SINGING BIRD

I've heard the lark soar high at morn,
Heard his song up in the blue;
I've heard the blackbird pipe his note,
The thrush and the linnet too.
But none of them can sing so sweet
My singing bird as you

  Ah-ah-ah-ah-ah, Ah-ah-ah-ah-ah
  My singing bird as you.


If I could catch my singing bird
I would warm him on my breast;
If I could catch my singing bird
In his own cozy nest.
For none of them can sing so sweet
My singing bird as you

  Ah-ah-ah-ah-ah, Ah-ah-ah-ah-ah
  My singing bird as you.


Discussion:
FP: Hoo.
PK: What is that called.
FP: My Singing Bird
PK: My Singing Bird. And where did you learn that?
FP: I got that when I was about four year old, from my father again. All them songs is got from
PK: Well, did he compose it or...
FP: Oh, no, no. Where he got it I suppose I don't particularly know, you see? It may have been from my grandfather, because there is a lot from my grandfather too, you see.
PK. Hmm
FP: But that's er, that's My Singing Bird. We generally sometimes play and sing these. It's not often that there is a piper does it, you know. Just for out own reason.



Source: McPeakes' recording by Peter Kennedy 39:01 at Peter Kennedy Collection (start 39:01)