We are first introduced to Barnard's Inn in Chapter 21 when Wemmick takes Pip to see his new lodgings. We see another example of Pip misinterpreting his surroundings: he is expecting a grand hotel, but the reality of Barnard's Inn is very different:
Whereas I now find Barnard to be a disembodied spirit, or a fiction, and his inn the dingiest collection of shabby buildings ever squeezed together in a rank corner as a club for Tom-cats.
It is key to focus on how Dickens builds up the picture of Barnard's Inn, assocating it with decay and dilapidation.
We entered this haven through a wicket-gate, and were disgorged by an introductory passage into a melancholy little square that looked to me like a flat burying-ground. I thought it had the most dismal trees in it, and the most dismal sparrows, and the most dismal cats, and the most dismal houses (in number half a dozen or so) that I had ever seen. I thought the windows of the sets of chambers into which those houses were divided, were in every stage of dilapidated blind and curtain, crippled flower-pot, cracked glass, dusty decay, and miserable makeshift; while To Let To Let To Let, glared at me from empty rooms, as if no new wretches ever came there, and the vengeance of the soul of Barnard were being slowly appeased by the gradual suicide of the present occupants and their unholy internment under the gravel.
Aspects to note here are the choice of diction (words such as "melancholy" and "dilapidated", the repetition of "dismal"). Details likewise contribute to a decaying picture, and in particular notice the alliteration of "dusty decay" and "miserable makeshift", all adding to the scene of desolation. The description of the square as a burial ground links Barnard's Inn to the graveyard scene at the beginning, and the overall picture of decay links it to Satis House, an impression that is only strengthened by the discovery that Herbert Pockett was the blond youth that Pip fought against. My favourite detail in this passage is "disgorged", an implied metaphor making it seem as if Pip and Wemmick are vomited out into the central square - a highly attractive image :-)