It's in Tawney's collection _Grey Funnel Lines_. According to his notes, Blue is a brand of Maltese beer, and Corradino is the naval prison in Malta.

His version has "I don't want your sherry" for "You can stuff your sherry". And it has the following after that stanza:

The OD he blushed crimson,
The Cairo Bar it was packed,
And every matelot started whispering:
"I bet that OD's just been cracked."

and then

Blondie got into a di-so,
She rowed round to Bighi Bay,
She went aboard the Warspite
And took her fifteen-inch away.

(No rooty-toot-toot for her!)

The rest is pretty much as you have it, but there are two alternative final stanzas:

Now this is the moral to the story
As any matelot can tell,
Never run an OD winger
And a blonde barmaid as well.

or

Now this story has no moral,
It only goes to show what I've said,
That there's more than one Valletta-bound Jane
And they ain't in the blinking Med.