No -- or at least, if he did, he was coy about it. _Grey Funnel Lines_ is an anthology of 20th-century British Navy songs collected by him (a book, not an LP, in case you misunderstood). The only song in it that is explicitly his is the eponymous one at the beginning.

As to "Bighi Bay", that's the way it's spelled in the book, and it gets plenty of Google hits.

It's getting on dinnertime, but I'll copy the printed version presently.