In Blake's "London," the speaker doesn't really disappear, but I think you might be referring to the fourth stanza, which shifts to night and darkness.
The speaker is central to the poem, in that the poem consists of what the speaker experiences as he walks through London. This is true of the fourth stanza, as well as the others, so, again, he doesn't disappear.
The last stanza is set in darkness, though:
But most thro' midnight streets I hear
how the youthful Harlot's curse
Blasts the new-born Infant's tear,
And blights with plagues the Marriage hearse.
Concerning this fourth stanza, the enotes Study Guide on the poem says:
The final stanza of the poem is set in darkness—Blake is listening in the midnight streets to the cries of young prostitutes as they curse the men who victimize them, the wives who are equally victims, and the religion that forces people to think that they must marry and stay married no matter what. “London” ends on a pessimistic note in which Blake reviles the one sacrament that should offer hope to present and future generations: marriage. Instead of being predicated on love and mutual respect, Blake sees it as something that enslaves the body and soul in much the same way that stanzas 2 and 3 point out that English laws victimize the less fortunate.
If you weren't thinking of the fourth stanza, the only other possible stanza in which one might say the speaker disappears would be the third. I suggest that the "cry" and the "sigh" are still being heard by the walking narrator, but one might be able to argue that stanza three contains generalizations, rather than an actual cry and sigh. If you wanted to argue that the speaker really does disappear, stanza three would be the only possibility.
One of the most pleasing aspects of poetry and poets (and William Blake's London is no exception) is it's timelessness - a poem written hundreds of years ago can sound as if the poet is actually speaking to us, and has not died at all. Such is the beauty of the written word. Poetry is subjective, so to me, Blake has not disappeared and I hear his voice as fresh as he is in the present to me. For example, he uses the words "thro' midnight streets I hear" (not heard, or used to hear - but hear now, today.) This sounds to me like a conversation in the present where he is describing his everyday life and walks to me - where he still sees a future before him. Sadly, the voices we can both hear are not pleasant ones.
In my opinion, you could answer this in two ways. Either the speaker disappears right away, or he never does disappear at all.
At least literally, the speaker does not disappear at all in this poem. The word I appears in three of the four stanzas, including the last. All of the images are reported by the speaker -- he is the one seeing and hearing them.
In another way, though, you can say that the speaker disappears right away. The speaker is not interacting with any of the things he sees and hears. So, in that sense, he might as well not be there.