How does Charles Dickens use different characters to launch a critique of the social conditions in Great Britain, especially in London?

Dickens, who lived in London as an adult and spent parts of his childhood in London under sometimes adverse conditions, was a relentless critic of the social injustices of this imperial capital. His critique cuts across many of his novels.
For example, in an early novel, 1837's Oliver Twist, Dickens critiques the new Poor Law of 1834 by showing the humiliation and deprivation young children endure in a poorhouse orphanage. He depicts a character like Oliver as a normal boy who is made an outcast because the workhouse clothes he is forced to wear immediately identify him as poor and therefore someone to be despised. At the orphanage, as Dickens describes it, the children are underfed. Getting only one scoop of gruel and "desperate with hunger," Oliver asks for more food and is thrown out for his pains. On the streets, he is vulnerable and sucked into a life of crime. Dickens critiques a London society in which a few are very wealthy while many, even innocent children, are hungry, cold, and at the mercy of a criminal class. As Dickens writes of the London of the poor in this novel:

Some houses which had become insecure from age and decay, were prevented from falling into the street, by huge beams of wood reared against the walls, and firmly planted in the road; but even these crazy dens seemed to have been selected as the nightly haunts of some houseless wretches, for many of the rough boards which supplied the place of door and window, were wrenched from their position, to afford an aperture wide enough for the passage of a human body. The kennel was stagnant and filthy. The very rats, which here and there lay putrefying in its rottenness, were hideous with famine.

Likewise, A Christmas Carol, Dickens's famous novella, critiques the kind of social Darwinist hard-heartedness of a character like Scrooge, who wishes the poor would hurry up and die so as to rid the world of excess population. The story contrasts the wealth of people like Scrooge with the poverty of people like the Cratchits. Even though Bob Cratchit works full time as a clerk and gets only one day off a year, he can't afford the medical help needed to keep his young son Tiny Tim alive and can hardly feed his family.
Bleak House attacks a bureaucratic wealthy class that is incompetent in such vital areas as educating the poor and handling diseases, as well as in providing a decent legal system and decent housing for the poor. Dickens describes a London slum area, produced in part by the gross negligence of the ruling class, where poor Jo must live:

a ruinous place known . . . by the name of Tom-all-Alone’s. It is a black, dilapidated street, avoided by all decent people, where the crazy houses were seized upon, when their decay was far advanced, by some bold vagrants who after establishing their own possession took to letting them out in lodgings. Now, these tumbling tenements contain, by night, a swarm of misery.

Dickens was not a political radical, but he was a keen observer, relentless in exposing a side of life most middle-class readers did not often see.