Here's a section which really highlights the mass changes this had to London at the time: "The first shock of a great earthquake had, just at that period, rent the whole neighbourhood to its centre. Traces of its course were visible on every side. Houses were knocked down; streets broken through and stopped; deep pits and trenches dug in the ground; enormous heaps of earth and clay thrown up; buildings that were undermined and shaking, propped by great beams of wood. Here, a chaos of carts, overthrown and jumbled together, lay topsy-turvy at the bottom of a steep unnatural hill; there, confused treasures of iron soaked and rusted in something that had accidentally become a pond.
Everywhere were bridges that led nowhere; thoroughfares that were wholly impassable; Babel towers of chimneys, wanting half their height; temporary wooden houses and enclosures, in the most unlikely situations; carcases of ragged tenements, and fragments of unfinished walls and arches, and piles of scaffolding, and wildernesses of bricks, and giant forms of cranes, and tripods straddling above nothing......
"In short, the yet unfinished and unopened Railroad was in progress; and, from the very core of all this dire disorder, trailed smoothly away, upon its mighty course of civilisation and improvement."
The chapter referred to a visit being made to Staggs's Garden, an area in Camden Town where the railroad was being built: "Staggs's Gardens was regarded by its population as a sacred grove not to be withered by Railroads; and so confident were they generally of its long outliving any such ridiculous inventions, that the master chimney-sweeper at the corner, who was understood to take the lead in the local politics of the Gardens, had publicly declared that on the occasion of the Railroad opening, if ever it did open, two of his boys should ascend the flues of his dwelling, with instructions to hail the failure with derisive cheers from the chimney-pots."
I'd speculate that from his writing in Dombey and Son, Dickens wouldn't have been the greatest fan of the London Underground and like many Victorians may have expressed the same levels of dismay on its opening.
But then again, like most Victorians, he would have got used to it and developed the love hate relationship that most Londoners currently have with the Tube.
Update Thanks to @RehanQayoom for letting us know according to Peter Ackroyd who clearly knows more than a thing or two about Charles Dickens (being one of his main biographers), he did travel on the London Underground on what was known as the Inner Circle Line.