Alliteration fills the poem with music, which makes sense given that the title is "Singh Song"! It also works closely with consonance and assonance to create a poem that's simply fun to read aloud.
Some subtle alliteration here is just the result of the poet's choice to evoke an Indian accent (for example, "I do di lock" in line 4). Other moments are more striking, as with "chapatti" and "chutney" in the second stanza. These strong sounds ring out through the lines and suggest the speaker's excitement upon spending time with his new bride.
More alliteration appears as a chorus of disgruntled shoppers complains to Singh that "yor lemons and limes." Beyond simply sounding musical and a bit funny, the shared sounds of these words reflects the fact that the speaker doesn't really care to distinguish between fruits. To Singh, lemons might as well be limes, and vice versa—he's more interested in his wife than produce!
Later, the alliteration of "head high heel" in line 18 draws attention to Singh's wife tapping her feet upstairs, while the sharp /t/ sounds of "tiny eyes ov a gun / and di tummy ov a teddy" add a bit of bite to this description of her. And as the speaker describes sitting in the store at the end of the day, musical alliteration evokes an atmosphere charged with romance and magic. These lines are loaded with shared sounds, as Singh describes how "de precinct is concrete-cool" as he and his wife:
[...] sit on my silver stool
from behind di chocolate bars
vee stare past di half-price window signs
at di beaches ov di UK in di brightey moon —
This intense alliteration signals that the drudgery of the daytime has been dispelled by the power of the young couple's love. The sibilance here also gently evokes the hush of the evening, when the lovers finally get some time all to themselves.