London: around 1794—that's the short answer to the question of where this poem takes place. Word.
Well, if that's the short answer, what's the long(er) answer? Well, the longer answer is: the slums of London in 1794. Now the speaker of this poem doesn't have any specific area of London in mind, just any generic, dirty place where you might conceivably hear harlots cursing and babies crying audibly, a place where "plagues," in the loose sense of disease, might be more widespread, a place where grown men cry and almost everybody is "marked" by "marks of weakness, marks of woe." Simply put, this poem deals with the parts of London where lower class citizens, prostitutes, former soldiers who are now broken, and the like might congregate.
Okay, that's cool, but why not just call the poem "The Slums of London"? That's a good question—hang on a sec while we get William Blake on the line. Okay, he's just informed us that the poem is just called "London" because, while only some areas of London are characterized by these sorts of things, all of London will be plagued by them if things don't change. If the government doesn't stop starting wars and getting blood on its hands, and if the church doesn't stop getting blacker and blacker, the city will crumble into a big mess of poverty, disease, and all sorts of other, metaphorical "manacles." (Thanks for the 411 there, Blakey.)
Another way to look at this little issue is like so: The speaker describes a small slice of London; obviously, there were nice, clean parts of the city in 1794. By acting as though all of London could be summed up in 16 lines that describe some pretty horrific stuff, the speaker makes the point that a city like London can't simply be divided into good and bad, clean and dirty, rich and poor. The fact of the matter is, the bad parts of London are part of the same geographical space as the good parts, and the good parts are in some ways responsible for creating the bad (the blood on the palace walls, for example, links this royal residence with war, death, and all sorts of other bad things). London, like a chain, is only as strong as its weakest link.
On top of all this, it is important to know a thing or two about the historical circumstances of the 1790s. If you've read our "In a Nutshell" section, you know that things were really heating up back then, politically speaking. Revolution was in the air, largely as a result of all the upheaval happening across the water in France. Besides cracking down on the expression of revolutionary sentiments, the British government declared war on France in 1793, and would remain continuously at war with their long-time enemy for the next twenty years or so.
Besides all the political business, there was the social and cultural business. Socially conscious fellows like Blake not only had to worry about their repressive, war-mongering government, but also about things like child labor and a church that, from time to time, condoned barbaric practices like chimney sweeping (check out our "Detailed Summary" of lines 9-10 for more on this). Toss into the mix poverty, prostitution, and disease and you start to get an idea of why somebody like Blake would write a poem like "London." The combination of war abroad and all kinds of reprehensible stuff at home, made for a rather tumultuous historical climate.