When a character is as pompous and self-interested as Uncle Pumblechook in a Dickens novel, the author is almost always using them to satirize a "type" of character from everyday Victorian life; in this case, a privileged blowhard. When Pip is told that Pumblechook will take him to meet Miss Havisham to "make his fortune," in chapter 8, a scene of the most laughable stuffiness occurs. Pip tells the reader that he was "trussed up" in his "tightest and fearfullest suit" and
delivered over to Mr. Pumblechook, who formally received me as if he were the Sheriff, and who let off upon me the speech that I knew he had been dying to make all along: “Boy, be for ever grateful to all friends, but especially unto them which brought you up by hand!”
Pumblechook receives Pip (who is often referred to by his family as being incurably criminal) "like the Sheriff": he means to send him off to a correctional facility with a sanctimonious speech about being "for ever grateful to friends." Of course, Pumblechook is not a policeman, but merely a "peppercorny and farinaceous" old merchant, as Dickens goes on to describe him in the next chapter.
Pip, reflecting on this instance from the "future" of the novel's narration, remarks that he knew Uncle Pumblechook had been "dying all along" to preach to him about how grateful he should be for this opportunity. The reader gets the sense here and elsewhere that, in an instance of dramatic irony, Pumblechook thinks he's very important and that everyone takes him seriously. It's clear from the tone Pip strikes here, though, that that isn't his view.
The author describes Pumblechook in terms of ridiculous self-importance, lampooning men of his time who came from "new money" (not inherited wealth) with pretensions to upper-class airs, and with patronizing and undeserved moral superiority. Further, Dickens indicates that Pumblechook is materialistic, selfish, and self-absorbed in all his habits. When Pip joins him for breakfast before heading to Satis House, he says he consides Pumblechook "wretched company," as his
conversation consisted of nothing but arithmetic [...] while he sat at his ease guessing nothing, and eating bacon [...] in a gorging and gormandizing manner.
Uncle Pumblechook here and later is characterized by Pip's dramatically ironic accounts of his excess and lack of self-awareness. He preaches abstinence and thrift in others while "gorging and gormandizing," telling Pip to be grateful for the meager amount he gets while Pumblechook stuffs himself with bacon.
The dramatically ironic motif of "beggaring," or stripping everything from a person, comes up several times in the context of playing games in Great Expectations. When Pip and Estella are asked to play cards to entertain Miss Havisham, this conversation follows:
Miss Havisham beckoned her to come close. [...] "Let me see you play cards with this boy.” “With this boy! Why, he is a common labouring-boy!” I thought I overheard Miss Havisham answer – only it seemed so unlikely — “Well? You can break his heart.” “What do you play, boy?” asked Estella of myself, with the greatest disdain. “Nothing but beggar my neighbour, miss.” “Beggar him,” said Miss Havisham [...]
The "game" of beggaring that Havisham actually wants is to see the protagonist emotionally impoverished, as the reader and the younger Pip of the story later learn. Miss Havisham, having been scorned in love, has set herself the lifelong task of ruining men's lives. The most valuable commodity to her is not the money she possesses, but the affection and devotion of men which she can then destroy. Lacking the power to do so directly, she grooms Estella into her instrument for "beggaring" men and boys, stealing all their emotional capital and ruining their lives.
The idea that she should play with Pip horrifies Estella, as he is a "common laboring boy." As Pip is already "common" and comparatively penniless, the idea of wealthy Estella "beggaring" him is particularly ironic here. This irony is doubled if one considers that Pip—who has a lot of real familial love in his life—is far "richer" in Miss Havisham's terms than Estella or Havisham herself. Pip may be a common "laboring" boy, but the prize Havisham wants to win is not money he could get from labor; it's his heart.