What is a milkman doing in a poem about a romantic relationship? Well, despite the cliché of bored housewives having trysts with their milkmen, there probably isn't a sneaky affair going on here. Did you notice that both times he appears, he is associated with the daylight? Let's see what he's doing in both cases:
- Lines 8-9: The milkman's arrival seems to be unwelcome, since the stairs "writhe" under his feet, which shows yet another part of the studio that is in disrepair. (It also shows us an example of personification.) He comes at 5:00AM, right around when the daylight comes to shed light on the food scraps on the table. So maybe he, like the daylight, is a witness to the way the woman is living, and a reminder (because somebody else sees it) of what is in need of repair.
- Lines 25-26: Here the connection between the milkman and the daylight is highlighted through a simile. The woman feels the daylight coming like a "relentless" milkman. Both the daylight and the milkman seem to symbolize the reality of the woman's situation—and neither one is pleasant.