Well Chappell states "A copy of the ballad is in the Bagford Collection, entitled "A lamentable ballad of Little Musgrave and the Lady Barnet, to an excellent new tune.""

So Chappel seems to have thought that the tune was in the Bagford collection.

What remains of The Bagford collection is in the British Library, but much of it has been lost, according to the BL website. And it doesn't appear to have been digitised.

In any case Chappel also states "The tune is the usual traditional version." Which implies to me that he thought the tune was already old - one doesn't refer to a recently written tune as traditional. He wrote this in 1855 so that implies he thought it was written much earlier than 1827.

It seems to me at the least to be highly probable that the tune is pre-19th century and likely that it is 17th century.

Dave