I hope you were not holding your breath for a response, though I am surprised nobody seems to know. The tune is called 'Tom Bowlin': 'here a sheer hulk lies poor Tom Bowlin, the darlin' of our crew .....' As Tom Bowling it was composed by Charles Dibdin. Most of Morley's A Sea Breeze is included in Sir Henry Wood's Fantasia on British Sea Songs as played at the last night of the proms. The two versions are so much the same that they are even in the same keys. You can take your banjo with you when it's scheduled to be played on the TV and play along yourself.