"The cuckoo is a pretty bird, she sings as she flies; she brings us glad tidings, and she tells us no lies." Many versions are women's complaints about men's false hearts (usually similar to "The Wagoner's Lad/Old Smokey")
Legends about the cuckoo bringing in summer (and infidelity) are common and early.
The cuckoo loves warmth, and so arrives late during migration; it is thus held to signal summer. Certain species of cuckoo also lay their eggs in other birds' nests (whence probably the word "cuckold"), hence their association with lustiness.
The legend is ancient; Alcuin (died c. 804) wrote a piece, "Opto meus veniat cuculus, carrisimus ales," in which spring begs for the cuckoo to come. And Alcuin was English. But he worked in Charlemagne's France, and wrote in Latin, so we cannot prove that the idea was that old in England. But we do have the very old English song "Sumer Is I-cumen In"; showing that the cuckoo legend had made it to England by then; see the entry on that piece for more details on the dating.
Outside England, we find a number of other songs on the theme: Maud Karpeles, _Folk Songs of Europe_, Oak, 1956, 1964, p. 115, prints "L'inverno e passato," "Oh past and gone is winter, And March and April too, And May is here to greet us And songs of the cuckoo.... May's the month for lovers And songs of the cuckoo" (Italian, from Switzerland), as well as "Kukuvaca," "Cuckoo, cuckoo, sings the cuckoo," in which a girl asks a mower, "Have you cut the grass for me?" (p. 217, from Croatia). - RBW