There are also versions of that localized to London and Edinburgh. The London one is by far the oldest recorded (it's in some versions of The Merry Muses of Caledonia, I think from the early 19th century). The Edinburgh one is the Greig-Duncan collection.

There is a Scottish tune of that name in the Skene Manuscript (early 17th century), though it's closer to the Northumbrian "Little Fishie" than to any modern "Spanish Lady" song.

The modern tune seems to be in the same family as "Donal Don" ("...may he never lack a scone") which has several names as a Scottish dance tune.