Dickens is saying that the unpleasant appearance of the Court of Chancery is understandable, since it mirrors (or serves as a physical emblem of) the way the court functions.
The Oxford English Dictionary has this under well:
II.8. Usually with modal verb, esp. may.
II.8.a. With good reason; naturally; as a natural result or consequence.
II.8.a.i. In an independent statement. Sometimes in initial position, with inversion of verb and subject.
“Well, Adv., Sense II.8.a.i.” Oxford English Dictionary, Oxford UP, December 2023, https://doi.org/10.1093/OED/9198914621.
The OED provides these examples, among others:
1611 Well may she bee paralelled with the euer-renowned Zenobia.
J. Speed, History of Great Britaine ix. xxiv. 881/1
1849 The government did not venture..to enforce a regulation of which the legality might well be questioned.
T. B. Macaulay, History of England vol. I. iii. 368
2005 Given the racist climate of the south, one might well wonder why white artists would want to sing blues in the first place.
D. Weissman, Blues: Basics iii. 76
So Dickens is saying that all these unwelcoming aspects of the Chancery Court are a natural reason or consequence of the way it works. The passage goes on:
This is the Court of Chancery, which has its decaying houses and its blighted lands in every shire, which has its worn-out lunatic in every madhouse and its dead in every churchyard, which has its ruined suitor with his slipshod heels and threadbare dress borrowing and begging through the round of every man’s acquaintance, which gives to monied might the means abundantly of wearying out the right, which so exhausts finances, patience, courage, hope, so overthrows the brain and breaks the heart, that there is not an honourable man among its practitioners who would not give—who does not often give—the warning, “Suffer any wrong that can be done you rather than come here!”
Charles Dickens, Bleak House. 1853. Chapter 1. Accessed at Project Gutenberg, 12 March 2024.
The workings of the Court of Chancery are gloomy, dispiriting, and harsh, and the physical appearance of the building that houses the court mirrors that. It is therefore with good reason that the building appears as it does: dim, foggy, and cheerless.