First, let's look at the poem one stanza at a time.
"I wandered through each chartered street,
Near where the chartered Thames does flow,
A mark in every face I meet,
Marks of weakness, marks of woe."
In the first stanza, William Blake is wandering through London and noticing that the look on people's faces gives away a life of suffering, weakness, and sadness. William Blake lived during the industrial revolution in England, which transformed urban centers like London into industrial powerhouses. While the industrial revolution was beneficial to England's economy as a whole, it did have the unintended consequence of widening the gap between the social classes. Throughout William Blake's poem "London", we will see evidence of the downside to the industrial revolution to the poor people of London.
In every cry of every man,
In every infant's cry of fear,
In every voice, in every ban,
The mind-forged manacles I hear:
In this stanza, Blake is talking about how in every man's voice he can hear pain. The phrase "mind-forged manacles" is very interesting- a manacle is a metal chain meant to bind someone (think handcuffs). A manacle forged by the mind would be a limitation set by your own imagination, or self-limitation. In the lives and cries of all Londoners, he sees people holding themselves back, suppressed by their own society and unable to rise above poverty.
How the chimney-sweeper's cry
Every blackening church appals,
And the hapless soldier's sigh
Runs in blood down palace-walls.
This stanza is especially helpful in pin-pointing different roles and jobs in industrial England. There are chimney sweepers no doubt lamenting their position (as sweeping chimneys is a pretty dirty, gritty job and highlights the dirty, gritty industrial London). He also references a blackening church, which could represent the corruption of the church as a whole. In industrial England, the church would help send children out to do jobs as, you guessed it, chimney sweeps, so in the first part of this stanza Blake is taking a stab at child labor and the church. The reference to a hapless soldier no doubt means that despite the problems in London, soldiers are powerless to do it against a government that is stained in blood (figuratively, not literally).
But most, through midnight streets I hear
How the youthful harlot's curse
Blasts the new-born infant's tear,
And blights with plagues the marriage-hearse.
But above the poverty and pain, child labor, social problems and industrial grit, Blake notes the existence of young harlots, or prostitutes. Their presence is so strong that they can even drown out the sound of new born babies, who are being born into such a cloudy and gritty world. The overall impression Blake is giving is that London is a dirty, gritty place where people are limited by their own imaginations and minds (mind-forged manacles) and that society as a whole is doomed to poverty, corruption, and general evil. It's a very provocative poem that highlights social problems and the negatives of industrialization in one of the world's most famous cities.
To go along with the other answer (the other person basically said it all) - William Blake was a Christian poet. Everything he wrote started with a Judea-Christian background. When he wrote London, he was criticizing the church for giving a deaf ear to its surroundings and for using innocents (young boys as chimney sweeps, young girls as prostitutes) for profit.