Earthen jugs formerly used in public house for drawing ale: they had the figure of a man with a large beard stamped on them; whence probably they took the name: see ben jonson’s plays, bartholomew fair, &c. &c. Dutch earthen jugs, used for smuggling gin on the coasts of Essex and Suffolk, are at this time called grey beards.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Gregorian Tree * Grey MareNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes