Roy Palmer prints a slightly different set in The Oxford Book of Sea Songs (1986), now revised and reprinted as Boxing the Compass. He comments:
"Steve Gardham recorded this from Thomas Calvert of Runswick Bay, North Yorkshire, in 1971. The song, which seems to have been a particular favourite in the Whitby area (though Cecil Sharp had a version from Middlesex, attached to a dance), was issued on a broadside printed in 1837-8 by W. and T. Fordyce, Newcastle, under the title of Caller Herring. This in turn loosely derives from a song of the same name by Lady Carolina Nairne (1766-1845), published in 1824 to a tune by Nathaniel Gow (1777-1831), based on 'the original Cry of the Newhaven fish wives, Selling their fresh herrings in the streets of Edinburgh'. Gow's tune was issued as a shilling music sheet for piano in c.1802."
The Fordyce sheet can be seen at Bodleian Library Broadside Ballads:
Caller Herring Printed c.1840 by W. & T. Fordyce, Dean Street, Newcastle.
Steve Roud's Folksong Index also refers to sets noted by Colin Wharton (from Frank Wetherill of Whitby, in 1961; probably the one quoted above) and three from Somerset (rather than Middlesex) in the first decade of the 20th century, two of which were collected by Sharp. A set of Lady Nairne's piece (missing two verses) is in the DT: CALLER HERRIN'