Alliteration adds music and emphasis to the poem's language. In doing so, it highlights the bittersweet nature of the speaker's daydreams: these reveries are lovely and lyrical, yet also distant and fleeting.
Alliteration also makes certain moments and images feel more important. In lines 5-6, for example, sharp /c/ and /p/ alliteration make the image of the speaker flying away from England sound all the more exciting and intense:
with a credit card and a warm coat you will leave
on the plane. The past fades like newsprint in the sun.
Alliteration often works alongside the related devices consonance and assonance to make the poem's language even more powerful. Take lines 8-9:
on the wrong side of your eyes. A beautiful boy
in the bar on the harbour [...]
The intensity of the poem's language sticks out to the readers' ears, just as this image sticks out in the speaker's mind. The same thing happens with "blue bridge" and "six swans" in the poem's final stanza: alliteration calls attention to these very specific images, highlighting how clearly they appear in the speaker's imagination.
Elsewhere in the poem, sonic devices convey the actual sounds of the scene the speaker is imagining. Take lines 13-15, where growling /r/, popping /p/, and hissing /s/ sounds (in the form of both alliteration and internal consonance) evoke the "rasp of carpentry" that the speaker describes:
Sleep. The rasp of carpentry wakes you. On the wall,
a painting lost for thirty years renders the room yours.
Similarly, the poem essentially turns up the volume on its own language in lines 16-18 in order to convey the intensity of all the "sounds" the speaker hears on their imagined walk to and from their old job. There's alliteration ("passing"/ "practicing," "sounds"/Seagulls"/"scales"/"swap," "for a fish," etc.) plus plenty of consonance and assonance ("Apt"/"passing"/"practicing," "Seagulls"/"bells"/"flute," etc.). All these repetitive sounds make the passage more melodic, suggesting that the speaker finds all these familiar noises pleasant and comforting.