I've copied the music which was on the abc site and changed it a little to match what the Copper Family sings. It's an unusual song; the first verse is eight measures long, the second is twelve, and the third is twenty. Although it's in 6/8, it has occasional measures with only 3 eighth-notes in them.

We get used to the distinctive music of the refrain (the primrose blooms), but then that music is used in the verse part about the milkmaid. Finally, the last refrain is missing.

It's still a nice song, but it's not a folk song. It's an art song. Written out, it's about 80 measures.