No relation to "Little Brown Jug" by Winner.
Neither is this one, also from England. About ale, so I will post it here.

Lyr. Add: Brown Jug

Dear Tom, this brown jug that now foams with mild ale,
(Of which I will drink to sweet Nan of the vale)
Was once Toby Philpot, as thirsty a soul,
As e'er crack'd a bottle, or fathom'd a bowl,
In boozing about 'twas his *praide to excel,
And among jolly topers he bore off the bell

It chanced in the dog days, as he sat at his ease,
In his flow'r woven arbor, as gay as you please,
With a friend and a pipe, quaffing sorrow away,
And with honest old stingo was smoaking his clay,
His breath-doors of life on a sudden were shut
And he died full as big as the Dorchester butt.

When long in the ground his old carcase had lain,
And time into earth had resolv'd it again,
A potter found out, in his covert so snug,
And with part of fat Toby he form'd this brown jug;
Now sacred to friendship. to mirth, and mild ale,
So here's to my lovely sweet Nan of the vale.

Bodleian Ballads Catalogue, Harding B17(40b), printed by T. Birt, London, 1828-1829. *Spellings not changed. Also printed by J. Pitts, London, ca. 1819-1844.
Another website dates the song to 1761, and says it may have given the Toby Jug its name. Brown Jug (error here- 'soaking' substituted for smoking). No tune mentioned at either website.