Okay, here it is, but if it turns up now I'll be reight narked!

Come all ye jolly seamen, a tough old Tar I am,
I'll sing ye of a fight, my boys, fought in the Nottingham.
'Twas by a brisk young Captain, Phil Saumarez was his name,
And he was bent, with bold intent, old England's foes to tame.

On the 5th day of October, our anchor we did weigh,
And from old Plymouth Sound, my boys, we shaped our course away.
Along the coast of Ireland, our orders were to go,
The seas to cruise, and none refuse, but boldly fight the foe.

We had not been out many days before we chanc'd to spy
A sail all to the westward which drew to us full nigh
She hail'd us loud in French, my boys, and ask'd from whence we came,
'From Plymouth Sound, we've just come round and the Nottingham's our name.'

'Are you a man-of-war,' they said, 'or a privateer maybe?'
'We are a man-of-war,' said we, 'and that you soon shall see.
So haul up smart your courses, and let your ship lie to:
If you stand out, or put about, we'll sink your ship and crew.'

The first broadside we let them have we made the rascals quail:
The next their yards and topmas'es came rattling down like hail.
We drove them from their quarters, their captain frantic grew,
He curs'd our shot, it came so hot, 'Mille diables! Scare bleu!'

We fought them seven glasses when, to add to all their fears,
The shout was raised for 'Boarders!' and we gave three ringing cheers:
Down came her flag, we took her; her name it was the Mars.
The French be damned, they ne'er can stand and fight with British Tars.

Not perhaps as well crafted as some of its antecedents, but at least based on a real incident and written by the captain himself, if a little over-self-congratulatory. It goes perfectly to the stirring 'Dolphin' tune that I know.

It is the original of Roud 690 and those versions that have Somerville/Somerwell as the captain or similar, that is obviously the folk process working and not a deliberate alteration like most of the other versions. It appears that Jon's family version is based on the original of 1746 whereas those that go under the following titles have
most likely been rewritten by broadside hacks, not that they made a bad job of it. I've sung at least one version.

Lord Exmouth
The Dolphin
The Irish captain
Shakings
Liverpool Play
Tha Saucy Dolphin
The Lion Man-o-war
Bold Wasp
The Liverpool Privateers
The Royal Delamore

An American development is 'Bold Daniels'

BTW some of the other ships like the Wasp, the Lion and the Dolphin were real ships at the time their versions were rewritten but the event obviously doesn't apply to them, they're just another example of the printer's hack after an easy shilling.