The opening of the poem sets up its premise: the reader will accompany the speaker on a walk through London, seeing and hearing what the speaker perceives. The verb "wander" makes the walk seem almost casual or aimless. This helps make the misery that follows seem like an everyday kind of misery—this world of poverty and pain is just what people will find in London whenever they walk through it.
Of course, we don't know yet that the city is such a dismal place; instead, these first two lines merely hint at its oppressiveness. To "wander" also suggests a kind of freedom, an idea which is put under strain by the word "charter'd." A charter is a legal document, granting or denying powers or access (to a particular plot of land, for example). In this one word, the speaker suggests what he or she hates most about modern society: the way it restricts and devalues human life. The "charter'd streets" specifically hint at the way London is a kind of cage, keeping its inhabitants within the confines of their pain. The diacope created by the word's repetition in line 2 reflects the way that this cage is inescapable. The streets, then, represent physical city limits that, in turn, hint at the mental limitations of the "mind-forg'd manacles" introduced in line 8.
Line 2 carries on with "charter'd" by now applying it to the Thames. The Thames is the river that flows through London, and it is a key part of the social fabric of the city. It's still pretty dirty now, but back when Blake was writing it would have been even worse—full of filth, waste, and even dead bodies. Here, the Thames acts as a kind of symbol in reverse: rivers are often symbols of natural beauty freedom, but in the poem the Thames only adds to the sense of misery, limitation, and restriction. This symbolic subversion is clear in the grammar of the line itself: The open assonance of "does flow" almost creates a sense of a river running freely, but it is immediately cut short by the harsh end-stop. The punctuation imposes its limits on any short-lived suggestion of freedom.
It's quite possible that the use of "charter'd" is an allusion to Thomas Paine's Rights of Man. Paine's book was a strong expression of support for the principles of the French Revolution (1789), and in this book he makes a remark that quite possibly informs this poem: "Every chartered town is an aristocratical monopoly of itself." In other words, the layout and organization of a city reflect its imbalance of power, power which is concentrated in the hands of a small ruling class.
Of London specifically, Paine makes another remark whose echo can be found in Blake's poem: "It is a market where every man has his price, and where corruption is common traffic." Worth noting here is that in the poem's first draft, both instances of "charter'd" read "dirty" instead. "Charter'd" must have seemed to better reflect the specific points about London's oppression that Blake wanted the poem to make.