I'm with you Joe.
I have a study of the ballad, Roud 2433. There is an 18thc broadside in the Madden Collection of 6 double stanzas, generic title 'A New Song' (Maddening isn't it?)
The ship is The Goldsprit of Plymouth and the captain is Capt. Farmer.

My master title is as the Penguin Book of Folk Songs 'The Royal Oak'.
Other titles include

• The Marigold
  
• Turkish Men of war
  
• The Good Luck Ship
  
• Captain Mansfield's Fight
  
• The Twenty-fourth of February

There are good historical notes on it in Baring Gould's Songs of the West, Nettl's Sing a Song of England, and on associated earlier pieces in Roy Palmer's Oxford Book of Sea Songs.