The poem sets up a strange, quiet scene: Death is simply out walking, back and forth, in the company of a watchmaker. The watchmaker is a fitting companion, since he deals in time, and time is what Death collects. Then the poem turns to something the speaker has been told rather than seen: a river he has never laid eyes on, sitting comfortably inside "a great and dirty pipe."
The title suggests the river is the Fleet, which is a real river in London, though the poem itself never says where it flows. What matters is the image. A river is something wild and living, yet here it has been tucked underground and made to feel at home in a drain. The speaker seems fascinated, even a little unsettled, by that idea of adapting to confinement.
The mood is calm, dry, and faintly eerie. Nobody panics. Death is casual, the speaker listens, and the thought lingers that people, too, might get used to the pipes they end up in.