Edinburgh was burnt to the ground (mostly by English armies) several times. The nearest in time to 1580 was the invasion under Edward VI in 1547 - this involved greater loss of life than any other conflict between England and Scotland (by a very large margin) and would certainly have been remembered both sides of the border a generation later. (I don't think any other war had a higher Scottish death toll until WW1). A triumphalist ditty like that would make a LOT of sense for English kids to sing.