If you take the last 4 centuries this is probably the most widely used tune, even surpassing Villikins. In the 16th century it was used for 'King John and the Abbot of Canterbury' now a Child ballad. In the 17th century it was widely used under the title 'A Cobbler there was'. By the 18th century and into the 19th it was being used for just about every other song (not necessarily folk songs). As Ray says it is usually referred to just as 'Derry Down'. The most common usage I can think of on the folk scene is arguably 'The Dreadnought'/'La Pique'/ 'Flash Packet'. It'll be in the DT

It's of a flash packet, La Pique was her name,
All in the West Indies she bore great fame,
For cruel bad usage in every degree,
Like slaves in the galleys we sailed the salt sea,
Derry down, down, down, derry, down........

Probably lots of others but can't think of them at the moment.

It was so popular that apart from being used for stirring derring-do songs which it goes best with, it was used for comic songs and all sorts of subjects. Weird!