In 19th-century England, you'd go to a pot-shop
— or, more commonly, a pothouse
— to enjoy some ale served in big drinking cups known as tankards or pots. A pothouse is a small alehouse (that serves just alcohol) or tavern (which also offers food).
In The Pickwick Papers, Mr. Pickwick asks Ben Allen and Bob Sawyer to delay their meeting with Arabella and Nathaniel:
To this they very readily agreed, and the proposition was accordingly acted upon; Mr. Ben Allen and Mr. Bob Sawyer betaking themselves to a sequestered pot-shop on the remotest confines of the Borough, . . .
And in Thomas Hardy's Jude the Obscure, Jude and Sue consider taking a different Arabella's small son into their home:
I feel that, anyhow, I don't like to leave the unfortunate little fellow to neglect. Just think of his life in a Lambeth pothouse, and all its evil influences, with a parent who doesn't want him . . .