William Blake, born in 1757, came of age at the outset of the Industrial Revolution (roughly 1760 to 1820), which was marked by an unprecedented population increase, a drop in living conditions for the already impoverished, and an increase in pollution and child labor. Blake lived most of his life in London, so that was the area he was intimately familiar with, so yes...the poem is about London during that period.
It is snapshots of what he saw as he walked through the "charter'd" streets and River Thymes. By "chartered," he means "owned" or usurped for the use of business, suggesting that these were no longer simple public spaces; factories seemed to own and control everything. As he goes on, it's clear that they also affect everything.
As he walks through the streets, he hears cries of "weakness," "woe," and "fear." People already limited in their prospects were losing ground and rights ("in every ban, / The mind-forg'd manacles I hear"), forced to work in factories where their pay was based on what they were able to produce and where their production was governed by the speed of the machines (and their work hours were long). Industry was presumably a wonderful innovation, but he witnesses the despair it brought to millions.
The air pollution is even blackening the churches, which is symbolic of the destruction of simple lives and simple faith with the advent and promise of capitalism. The Industrial Revolution is, in essence, destroying London's--and the world's--social fabric, forcing more children to turn to selling their bodies to get by (become "youthful Harlots"), spreading diseases which in turn "blight with plagues [probably of the sexual variety] the Marriage hearse."