"Where the Picnic Was" contains frequent alliteration. Besides adding emphasis to particular lines, this device makes the poem as a whole more musical.
In the first stanza, the alliteration is pretty light: there's just "branch and briar" in line 3 and "sea" and "slowly" in lines 4-5. But things get much denser in the second stanza. After the /gr/ sounds in "the grass is gray" (line 11), there's a cascade of sibilant /s/ and /st/ words:
But the spot still shows
As a burnt circle—aye,
And stick-ends, charred,
Still strew the sward
Whereon I stand,
Try reading this passage aloud: all the /st/ words, in particular, make it sticky and tough to say. That difficulty seems to mirror the emotional strain of the passage, as the speaker confronts the "charred" remnants not only of a summer picnic but of his former, happier life. The harsh, hissing, unpleasant sounds also fit the ugliness of the imagery: the "burnt" grass, "strew[n]" debris, etc.
In the final stanza, /br/ and /st/ alliteration helps draw attention to one of the poem's key images:
And the sea breathes brine
From its strange straight line
These strong, repeating consonants evoke the consistency and durability of "the sea," which keeps "breath[ing]" no matter what—even as puny human lives come and go.
Finally, the shared /r/ sounds in "grassy rise" and "urban roar" (lines 26-27) help the poet underline a contrast: between the speaker's natural, rural landscape and the unnatural "roar" of city streets.