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).
What does pot-shop (from The Pickwick Papers) mean?
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 . . .