Carthy's version above appears to be a selection of verses (with some tinkering) of "May-Day Carol" (Essex), collected by J. A. Fuller-Maitland and "The Moon shines Bright" (Hertfordshire), collected by Lucy Broadwood, both published in their joint book, 'English County Songs', 1893.

See also ZN935| for another 'Bell-man' song in the broadside ballad index on my website.