Hi, Jim
All of this is in the White/Donaldson version, apart from the additions to the last verse, with other verses as well.

The plot thickens. Having looked more closely at my indexes I find I have another related song I recorded from an old lady in May 1972, but we're back with a female narrator with a female singing.

I once had a sweetheart, me a courting did he
He was so attentive as attentive could be,
One day he took me out for a walk by the sea,
Now let's go for a swim, my darling, said he.
We went in the water, and oh deary me!
I said how deep do you think the water might be
Just up to your expectations said he,
Oh, how he lied to me!

The recording is online at BLSA at C1009/9 C10. I'll check out the tune.

I noted she knew further verses but I failed to record them. Gnash! gnash!

The style of this piece is more 1890s to me.