I cant provide any further facts, but I am experienced at reading text written by people who are trying to hide their lack of knowledge. And one thing people really have lack of knowledge about is tunes.

The site you linked finally comes out and says:

"It was sung on the stage in a play called The Custom of the Manor in 1715, but it's doubtful whether a town composer made it, even though it's an unusual shape for a traditional tune. Most probably he lifted it from tradition."

Well, that writer might have thought the tune had an usual shape for a traditional tune, but I don't think so. It's got a usual shape for a kind of tune called a slow air. And it's my impression that the poor people of the British Isles have been composing slow airs for a long, long time while publishers, etc have paid almost no attention. So that tune could have been original in 1715 or it could have been around for a hundred years already.
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I hope you won't mind a suggestion. If you are going to sing this song for an audience, sing it more happily than Steeleye Span does it. That Steeleye Span recording could be about a battle or a massacre or the crucifixion. It's a happy song, so sing it happily. Your audience will pay more attention, I think.

You don't have to speed it up or make it trivial, but if you smile with your eyes as sing about dancing and making love, it will be a better song.