The "standard" version of "Cruising Round Yarmouth" was collected by Peter Kennedy from the great Harry Cox of Norfolk (1885-1971) and recorded by Ewan MacColl on the album "Blow, Boys, Blow."
It is the only available version to specify the locale as "Yarmouth."
Cyril Tawney was the first to record the version now called "The Fireship" in 1964. The mention of "merry Portsmouth town" indicates a naval origin.
Cyril Tawney kindly answered my inquiry in 1994 to say that his text and tune were exactly as collected by Patrick Shuldham Shaw in Shetland in the 1940s. While in the Royal Navy, Tawney himself collected a fragment of the song which he calls "Whale Island Anthem" in his book "Grey Funnel Lines."
Stan Hugill printed a similar text, but with a different chorus, in "Shanties and Sailor Songs" (1969). Hugill calls the song "Ratcliff Highway," though it differs considerably from the song in "Shanties from the Seven Seas."