Once these mixed-up threads have run their course someone ought to sort out the half-dozen different songs being presented. The other thread is nearly the same with a version of the children's song 'Here we come gathering nuts in May'in its midst. It would take some sorting out and combining with the other thread but would save a lot of confusion.

The original request was for a provenance and that has still not been addressed. John Mehlberg has my uncle's version which he picked up in the RN during the Korean War so just after WWII. Here is a verse and chorus of my uncle's version:

I took her gathering roses, roses, roses
Down by the old millstream.
I took her gathering roses, we took off all our closes
Down...

Oh don't do it tonight, my love, the moon is shining bright
The stars are twinkling in the sky, so high,
Somebody's watching us, they're watching you and I
So let's go round the corner and do it on the sly.

The nearest other tune I can think of is the 19thc song 'Granny's Old Armchair'