"Not Waving but Drowning" uses alliteration sparingly throughout. The first example is in line 1:
Nobody heard him, the dead man,
These two /h/ sounds have an exasperated, breathy quality to them. This is important for two reasons. Firstly, it relates to the frustration felt by the dead man at how he's always been misunderstood, even in death. Secondly, with the focus on breath, it also relates to the way to the mention of drowning (and death as taking the final breath).
The next example is line 5:
Poor chap, he always loved larking
This line is spoken by the crowd gathered around the dead man—the people who misunderstand both his death and the way he was during his lifetime. The playfulness of the two alliterating /l/ sounds (further supported by the consonance of "always") is ironic, because elsewhere in the poem the dead man desperately tries to communicate how he never "loved larking" (playing about)—or, at least, that his desperation was mistaken for friendliness and playfulness. In other words, he was "not waving but drowning" all his life.
In line 7, the poem returns to the /h/ sound mentioned above. This carries the same meaning, but is intensified: "him his heart gave way[.]" These /h/ sounds here are panicked and frantic, like the final moments before death.
Line 9 uses epizeuxis in the repeated "no," but this also creates an alliterative effect that emphasizes the word—and, in turn, stresses just how wrong everybody was about the man and his character.