We sang this song in kindergarten in England in about 1962. I'm sure it came from the BBC as one reviewer mentions. We had an end-of-term show in the local village hall and I got to sing it solo. Those were the days!

From what I remember these are the first two verses:

Oh once I heard a mermaid Sing
As I sailed the sea, the dee-ep blue sea
Oh once I heard a mermaid sing
As I sailed the briny ocean

Oh-h cabin boy come and play with me
As I swim the sea, the de-ep blue sea
Oh cabin boy come and play with me
As I swim the briny ocean

That's all I can remember, but it brings back very fond memories!