Fagin goes into "a maze of the mean dirty streets which abound in that close and densely-populated quarter" (19.4), and Sikes and Nancy drag Oliver "into a maze of dark, narrow courts (15.63). Just from these two examples, you can see that the labyrinth motif recurs frequently in Oliver Twist and, in both of these examples, it’s in descriptions of the city. Hmm, now why might that be? Well, besides the fact that the streets of London were (and still are) pretty difficult to navigate if you didn’t know your way around, it could be that the idea of the labyrinth just adds to the sense of confinement in the city. The original labyrinth of Greek mythology (you know, the one on Crete that was guarded by the Minotaur?) was used as a prison. So the labyrinthine and maze-like streets of London could suggest that the entire city is part of the same system of control and incarceration as the judicial system that literally imprisons people, and the parish system that confines poor people in workhouses.
Or perhaps the maze motif has more to do with criminality: Dickens seems to suggest that once a person turns to crime, it’s impossible to get back on the right track – just like in a maze. Take Nancy, for example: even when she’s repeatedly offered the opportunity to escape her life of crime, she refuses, saying, "I am chained to my old life. I loathe and hate it now, but I cannot leave it. I must have gone too far to turn back, – and yet I don’t know […]" (46.74). In this quotation, Nancy uses the metaphor of paths and crossroads, too – she says she’s "gone too far to turn back." So it could be that this later quotation is referring back to the earlier motif of labyrinths and mazes, and relating it to her life of crime. If that’s the case, then perhaps Dickens is suggesting that once you become a criminal, it’s like entering a maze – it’s difficult or impossible to get back out again.
Whether the mazes are suggesting that the city is a prison, or that criminality is inescapable once you turn to crime, the maze and labyrinth motif seems pretty pessimistic, doesn’t it?