I've been right through 2 volumes of Dibdin songs and nothing resembling it has popped up. There is a song called 'Blow high, blow low' but apart from that one phrase there is nothing in common.

I can't even see a song about piracy. They're all about the joys of being in the Royal Navy and all very sugary which is probably why very few caught on with ordinary ratings. They're full of clichéd terms, written for the theatre.

Having said that I have in the back of my mind a song that uses the chorus but without a title I'd be hard put to find it.

It is of course based on the 17th century original broadside anyway and Dibdin certainly didn't write that.