Symbolism, Imagery, Allegory
We find ourselves wanting to say this poor kid every time we want to explain something about the narrator—he's just such a sympathetic creature with his curious nature and abject isolation. His fixation on the little yellow wash-basin that is in his old room is just one example of how pitiable this (poor) kid is:
I thought I must have done something wrong and was there for a telling-off, but no: they told me only that they were no longer affluent, that we would all need to make sacrifices, and that what I would be sacrificing was my bedroom, the little room at the top of the stairs. I was sad: my bedroom had a tiny little yellow washbasin they had put in for me, just my size […]
My former bedroom at the top of the stairs was let out, and a variety of people passed through it. I viewed them all with suspicion: they were sleeping in my bedroom, using my little yellow basin that was just the right size for me. (2.3-5)
For him, the sink stands for a time when his parents still did things—like put in an appliance—just for him. They seem so preoccupied with other concerns by the time our story happens that they don't even notice when a new pet shows up—but back in the old days, when they had money, they paid enough attention to him to install a sink that's just the right size.
During Ursula Monkton's occupation of the room, the boy is disturbed that the little yellow washbasin can exist in such a den of iniquity, and he's unable to return to the room even after everything's all said and done.
There was now nobody sleeping in my bedroom at the top of the stairs. My mother asked if I would like my room back for a while. I said no, unsure of why I was saying no. I could not remember why I disliked Ursula Monkton so much—indeed, I felt faintly guilty for disliking her so absolutely and so irrationally—but I had no desire to return to that bedroom, despite the little yellow handbasin just my size, and I remained in the shared bedroom until our family moved out of that house half a decade later… (15.36)
The little yellow washbasin consistently harkens back to the past, be it a time when his parents were attentive to him or the time when Ursula Monkton arrived on the scene and really messed his life up. And though he presumably used it as a child to wash his hands and such, he can't quite rid himself of his past so easily.