According to Popular Music of the Olden Time (William Chapell, 1859), contrafacts to this are known as early as 1564 and include Delone's The Duchess of Suffolk's Calamity. I've only reprinted the first two stanzas; it's quite a long song. For those not up on their Aeneid: after Troy was sacked, Aeneas (a prince of Troy) wandered about the Mediterranean and spent some time in Carthage. Queen Dido wanted him to stay, but he felt a greater destiny calling him (helping to found the city of Rome, as it turned out); when he left, she built a great funeral pyre and threw herself into it.
When Troy town For ten years' wars Withstood the Greeks In Manful wise; Yet did their foes Increase so fast That to resist None could suffice Waste lie those walls That were so good And corn now grows Where Troy town stood.