Who wrote the nursery rhyme baa baa black sheep?

The first known publication of the rhyme was in 1744 in Tommy Thumbs Pretty Song Book. It is not known who the original author of the nursery rhyme was. The lyrics to the very original version are:

Bah, Bah a black Sheep,

Have you any Wool?

Yes merry have I,

Three Bags full,

One for my master,

One for my Dame,

One for the little Boy

That lives down the lane.