When the broadside hacks get hold of a song and start trying to update them to sound more contemporary they aren't too fussy about correlating the info, hence the jumble of information in the later versions, particularly pertaining to the Dolphin and the London.

I'm no maritime expert so this is just my take on the Liverpool mentions. As far as I can make out when two ships meet and exchange info they ask where each has come from. Though Liverpool wasn't a naval base the navy ships must have used the port a lot for things like supplies especially when cruising in the Irish Sea. So the 'London' man of war in the many broadsides could easily reply 'Liverpool' in answer to 'where and whence we came'.