Previously on Varney the Vampire: They chase after the vampire. It heals by moonlight. They spend tedious amounts of time trying to deny that it is a vampire.
Chapter 6 (A GLANCE AT THE BANNERWORTH FAMILY. -- THE PROBABLE CONSEQUENCES OF THE MYSTERIOUS APPARITION'S APPEARANCE.) is short again—only 2770 words, which is a little less than I write in a productive day. The title is not promising, however, and neither is the first paragraph, in which the narrator, having surrendered his long and dull soliloquies to the dialogue for the previous several chapters, returns with a vengeance to tell us all about the Bannerworth family.
The Bannerworths, as was briefly stated by Henry in Chapter 5, are not doing well for money. The family estate has been in dire straits for over a century, since the irresponsible ancestor in the portrait—who, if the plot continues at this rollicking pace, will doubtless be revealed as Varney somewhere around Chapter 47.
Henry's father became ill, and intended to sell the family property. Before his death, he confides in Henry that the money will allow them to "live like princes," but he leaves no clue as to where the money has gone.
Henry, now in charge of the estate, is offered a price far beyond its value by a solicitor on behalf of an unknown client. Against advice, the family refuses the offer, wishing to stay in their house.
The reason given is thus: conveniently, a dead rich relative offers Henry, George, and Flora money to travel in Europe. Also conveniently, a mysterious stranger arrives to save Flora in Italy when her horse slips as they ride up a mountain. His name is Charles Holland; he claims to be an artist, and begins to court Flora. He intends to visit her at their home after a two-year absence, and so Flora, who has (also conveniently) been left with no way to contact him, does not wish to leave for fear that he might miss her.
Mr. Marchdale, a distant relative of Mrs. Bannerworth, arrives on the scene. He is a traveler by nature, with no family of his own, and he settles down to live with the Bannerworths.
Suddenly the author remembers that there's a vampire, and that people are probably reading this chapter to find out more about the vampire and not the boring Bannerworth family. So we are reminded of how the reality of a vampire's existence will change the family—an implicit excuse for the family's repeated refusal to believe in such things.
And so ends the book's dullest chapter so far. Perhaps something will actually happen in the next chapter; but I wouldn't get your hopes up too high.