There is quite a symbolic importance of London in Great Expectations. The time period covering the events in Great Expectations is 19th century London, particularly the year 1860. During this time, the Industrial Revolution had reached its climax, and London was on its way to become the top power in the world, with inventions that propelled world history.
The best way to understand it as a modern reader is by locating what city in the 21st century is the most tech-savvy, cosmopolitan, culturally-varied, sophisticated and, above all, rich. Well, that was London in the mid 19th century. A small city that carried with it a lot of history, activity, atmosphere, and immense fortune.
Now, contrast that to Pip's humble beginnings in the marshes, where he was literally living the exact opposite of what life in London was like. London, to someone like Pip represents the ultimate milieu in terms of success. London is, in the novel, the equivalent of civilization; a world where only the most successful go and where all things are possible.
farewell, monotonous acquaintances of my childhood, henceforth I was for London and greatness;
Therefore, London offered the opportunities that so many would have wanted to succeed in life. London is also the conduit through which Pip goes back and forth in the quest for himself and in the process of letting go of his past. London is not just a city, but a social setting that separates the "haves" from the "have nots" in a very dramatic way.