Between chapters, Brownlow has found Monks at the Cripples and has brought him, with help from servants, in a carriage back to his (Brownlow's) house. Brownlow says that, if Monks yells or tries to get away, Brownlow will call immediately for the police. Monks appears calm but defeated.
Brownlow has captured Monk "off-stage," that is, this action is not narrated by the narrator. Perhaps, at this point, Dickens felt it was necessary simply to move the plot along, and to resolve certain aspects of Monks' and Oliver's fates.
It is revealed by Monks, when the servants have gone, that Monks is Brownlow's "father's oldest friend." This is, naturally, a shock to the reader but not to the two men in the scene. Brownlow also explains (aloud, and for the reader's benefit), that Monks' real name is Edward Leeford, and that a woman whose maiden name was Leeford, and was related to Monks' father, was Brownlow's wife, who now is dead. Brownlow says he is glad that Monks no longer goes by Leeford, since Monks has sullied that name.
Another, and perhaps the crowning, coincidence of the novel. Brownlow is not just a disinterested party—he has a relationship with Oliver's father, and in becoming Oliver's stepfather, at the novel's end, Brownlow is fulfilling a duty to a long-lost friend of his, one that that friend, Leeford, could never have anticipated being necessary.
Brownlow tells Monks that he has a brother—Monks does not at first admit that this is true. But Brownlow continues: Brownlow knows, he says, that Monks' father and mother were brought together in marriage by Monks' grandfather, that Monks' father never wanted the marriage, and that Monks is the only child of that union. When Monks was a boy of about ten, however, his parents separated, and his mother went to live in Europe, while Monks' father stayed in England. Monks denies that he knows this, too, but it seems clear that he does know.
Though Monks might be a fairly accomplished criminal, he is not nearly so good at lying as is Fagin. Brownlow then goes in for a great deal of explanation that is, of course, not necessary for Monks to hear, but is absolutely necessary for the reader to hear. Monks' denials allow Brownlow to outline the facts of the case in extreme detail.
Meanwhile, in England, Monks' father became friends with a naval officer with two daughters—one nineteen, and the other only two or three. Monks' father becomes engaged to the elder of these daughters. But Monks' father learned that he had inherited, from a relation in Europe, a good deal of money, and so Monks' father went to Europe to get it—but in Rome Monks' father became ill, and Monks' mother, along with Monks, went to join him there. In Europe Monks' father died of this illness and left no will, nor did he have a chance to marry the elder daughter of the naval officer. All Monks' father's money went to his wife and to Monks.
It is, of course convenient and necessary that the younger daughter of the naval officer be significantly younger than the other daughter, Agnes, as that younger daughter ends up being Rose, who is closer to Oliver's age than she is to Oliver's mother's age. Later it is revealed that in fact there was a will, which Monk's mother destroyed, and so Monks received his inheritance through a crime. There is then a suggestion that through this original crime Monk's became ensnared in a life of crime—that committing a crime morally tainted him in such a way that he could never stop committing crime. This puts Oliver's goodness in a new light, that he always refused to commit any crime even as a 10-year-old boy is what saves him. Dickens portrays criminality as a kind of trap—where a single act of criminality forces most people into an inescapable life of crime.
Brownlow knows this because Monks' father stopped to see Brownlow on his way to Europe to collect his inheritance. At this time Monks' father gave Brownlow the portrait of his love that hangs in the parlor—the picture of which Oliver was so enamored—and on Monks' father's death, Brownlow traveled to see this woman, only to find out that, before their marriage, the woman of nineteen and Monks' father had had a liaison, and the woman was pregnant. The woman's family abandoned her, because they were ashamed of her pregnancy before marriage.
Finally, the mystery of the portrait can be explained—the woman resembles Oliver so much because Oliver is her own flesh-and-blood. What is less clear is: why would Brownlow hang this portrait on his wall? Because it was important to a friend of his? Because Brownlow simply thought the image was a beautiful one? It's not explained, but the picture had to be on the wall so that Oliver could see it, and react to it.
Brownlow tells Monks that it was he, Brownlow, who took Oliver in off the street, and Fagin purposely withheld from Monks the name Brownlow, lest Monks should make the connection between the two. After Oliver was taken away by Nancy, back to Fagin's, Brownlow realized who Oliver was, and vowed to find him. Brownlow went to the West Indies because he believed Monks could be found there, but he did not find Monks, and so returned to London.
This, too, explains Brownlow's trip to the West Indies—which, again, may as well be a symbolic stand-in for a place so far away as to be almost like another planet. Thus Brownlow didn't go to the West Indies to escape Oliver, but rather to find out more information about Oliver's predicament.
Monks hears all this but still refuses to admit to his plans for Oliver. Monks tells Brownlow he cannot prove that Oliver is the child of Monks' father and this woman. But Brownlow says he can—he has found out that Monks' mother destroyed a will that did make mention to a possible child of his union with his fiancée. Brownlow has also heard that Monks destroyed bits of evidence he gained from Mrs. Bumble, "the only proof of Oliver's parentage." This knowledge is enough to link Oliver to Monks' father.
Brownlow never produces this will, but it's enough when Monks admit to it, to know that the will exists—presumably this is also enough to satisfy the authorities, who choose to allow Brownlow to administer this will, Brownlow then chooses to disburse half the will to Monks and half to Oliver, meaning that Brownlow is in a position of executoriship—which is of course possible, since Brownlow becomes Oliver's adoptive father.
Brownlow also declares, to Monks, that murder has been done on account of this secret—as Sikes, after all, killed Nancy because he feared that Nancy had given away the group (Fagin, Sikes, Monks, and the boys) to the authorities. The accumulation of all this information stuns Monks, who agrees, finally, that Brownlow's story of the events is true, and Monks says he will swear to it in a signed affidavit.
The final straw. One notes that, far earlier, Monks was reluctant to kill Oliver, as he felt this would inevitably drag the authorities into the affair. When Monks realizes that a woman has been killed, he knows there is nothing more he can do—the authorities will soon discover his plot, and he might as well surrender to a man more inclined to help him, namely Brownlow.
Brownlow tells Monks he will protect him if he swears to this version of events. Losborne then enters and says that they have found Sikes' dog and have used it to locate the murderer; Losborne, Brownlow, and Harry Maylie make haste to find Sikes and capture him. Losborne also says that the authorities are on the lookout for Fagin.
The novel approaches, briskly, its conclusion, after having wrapped up this lengthy expository conversation between Brownlow and Monks. The other characters will be filled in on these details later.