I bought Cyril's Grey Funnel Lines songbook, thinking it would be a collection of songs he wrote. I does have the lyrics of "Grey Funnel Line," but all the other songs are traditional sea songs. Good book, though.
the song is on Tawney's Navy Cuts CD. I have to go to a meeting now, but I should be able to transcribe the song this evening unless somebody beats me to it.

So sailors all, if you'd have her true,
Don't court your girl in the Navy blue.
For when you change to the sober grey,
You'll see her heart will turn the other way.

-Joe Offer-