These three locations figure differently into Pip's life. The Jolly Bargeman is the "public house" where Joe Gargery likes to go and smoke his pipe. In Chapter X Pip goes there to meet Joe who is having a drink with Mr. Wopsle and a stranger.
He was a secret-looking man whom I had never seen before. His head was all on one side, and one of his eyes was half shut up, as if he were taking aim at something with an invisible gun. He had a pipe in his mouth, and he took it out, and, after slowly blowing all his smoke away and looking hard at me all the time, nodded. So, I nodded, and then he nodded again, and made room on the settle beside him that I might sit down there.
But, Pip slips in the seat next to Joe; however, he notices that the stranger rubs his leg in a familiar manner--like the convict. Then, this man asks Joe several questions about his job and the area where they live. Unexpectedly, he stirs his drink with a file, and Pip is greatly disturbed as it is the file which Pip took from Joe the night that the convict ordered him to get him "wittles and a file." Significantly, Pip realizes the man knows his convict.
Mention is made of the Blue Boar, an inn in Pip's town in a couple of chapters, one in which Pip stays there before his trip to London; however, in Chapter XXVIII Pip leaves London after Joe's rather awkward visit. While Pip intends to apologize to Joe and stay at the forge, he instead goes to the Blue Boar, making excuses to himself. As he rides in the coach he again encounters convicts as two sit behind him, being transported. One man with a half-closed eye is the very same convict that Pip has seen as a boy at the Jolly Bargeman, and they talk of the two one-pound notes that were given to Pip.
"Yes, I was. Would I find out that boy that had fed him and kep his secret, and give him them two one pound notes? Yes I would. And I did.”
Although Pip knows the convict does not recognize him, he experiences great apprehension, a "revival of the terror of childhood." At the Blue Boar, Pip goes into the coffee-room and dines. There the waiter knows him and asks if he wants someone to fetch Uncle Pumblechook shows him a newspaper in which the pretentious Pumblechook has taken credit for Pip's good fortune:
.... It is not wholly irrespective of our personal feelings that we record HIM as the Mentor of our young Telemachus, for it is good to know that our town produced the founder of the latter's fortunesT
To Pip's amazement Little Britain is the address for the London office of the unscrupulous Mr. Jaggers. When Pip arrives in London in Chapter XX, his expectations are hardly met as the city is dirty, unnatural, and suffocating. Pip describes Mr. Jaggers's office as "a most dismal place" as it is lit only by a skylight.
There were not so many papers about, as I should have expected to see; and there were some odd objects about, that I should not have expected to see—such as an old rusty pistol, a sword in a scabbard, several strange-looking boxes and packages, and two dreadful casts on a shelf, of faces peculiarly swollen, and twitchy about the nose. Mr. Jaggers's own high-backed chair was of deadly black horse-hair, with rows of brass nails round it, like a coffin.
Pip imagines that the convict with the half-closed eye had "shuffled" along the greasy wall before his trial after he was "turned-out."
The Three Jolly Bargemen appears to be an establishment that serves at least drinks, but maybe also food. It is somewhat close to the forge because Pip, Orlick and Joe frequent this location. This location is where Pip sees the convict stir his drink with the file. It is also where Mr. Jaggers heads after leaving the Gargery forge when he presented Pip with the idea of his expectations. It is formally referred to as a public house.
The Blue Boar is also an establishment in the village Pip grew up in, however, this establishment differs because it also offers rooms. This is made clear because Pip uses this place when he visits home while he is staying in London.
Little Britian is where Mr. Jaggers office is located. This is close to the courthouse and it seems to be a run-down portion of town. Chapter 20 reports it's location as
"just out of Smithfield, and close by the coach-office."
Pip describes the street there as gloomy and Jaggers office space as dark.