I think that a Marxist read to Dickens' work could focus on the teachings of Gradgrind as a starting point. Marxist theory would suggest that the emphasis on "facts, not fancy" and the embrace of Utilitarianism becomes a justification for the abuses perpetrated as a part of capitalism. Capitalism and free market teachings that are such a part of financiers like Bounderby have become a means to oppress many. In Bounderby's case, Marxist theory would detail this in the personal and the social realms.
In Gradgrind's case, Marxist theory of capitalism as dehumanization extending to everyone who comes in contact with it can be seen in the cases of his children. Gradgrind has become dehumanized by capitalism in his teachings that have deemphasized human feelings and interactions, again making it easier for capitalism to perpetrate its abuses. At the same time, Grandgrind's children suffers under the realities of capitalism that are perpetrated in their father's teachings. Tom learns to use people as a means to an end, a condition of capitalism, while Louisa cannot value the emotional sensibility of human beings. For the Marxist, the condition in which the Gradgrind children emerge is a capitalist one where any hope of redemption in being is lost to a detached and alienated suffering in consciousness.