Why do you think William Blake never actually says the word "London" in the poem itself? Could this poem be about other cities?

William Blake probably doesn't ever say the word "London" in his poem because he does not need to name the city by name.  There is little doubt that the city is London based on the opening stanza.  

I wander thro' each charter'd street,

Near where the charter'd Thames does flow.

The direct naming of the Thames river clearly identifies the city as London, so there is no need to use the word "London."  

In regards to the second part of your question, "Could this poem be about other cities," yes I think the poem could be describing just about any other sprawling metropolis during this time period.  The poem describes the city as being crowded, dirty, depressing, and dangerous.  I've read enough about the industrial revolution to know that Blake's description of city life is not unique to London.  The poem could be about Boston or New York during that time, and his descriptions wouldn't change (other than the Thames river part).