This story is unusual in that it's the first time in a short story that Poe attempts to deal with characters who are not aesthetes or aristocrats. That said, the author chooses to take a third person viewpoint, as in 1832's METZERGERSTEIN, in contrast to his well known first person narration.
The story follows the comical misadventures of two drunken sailors, "Legs" and "Hugh," rambling about London during the "chivalrous reign of Edward III" (the early 1300s). Too drunk to notice where they're going, they ramble into a district marked off as contaminated by plague. The sailors don't encounter anyone suffering actual plague, though the district is full of "fetid and poisonous smells." They blunder into a building described as "the stronghold of the pestilence," where they find six beggars celebrating with various spirits. The beggars, all of whom have comically freakish appearances, have all given themselves lofty aristocratic titles, and their chief has identified with the plague itself by calling himself "King Pest." The sailors manage to throw the celebration into chaos before they run off, carrying one of the female beggars with them.
The tale seems more like a sketch than a narrative, whose main point is to contrast the low-class drunks with the equally inebriated beggars, who have assumed lofty titles and speak in a much more elevated tone. It utilizes the tropes that I've labelled "freakish flesh" and "weird families and societies."