This question is most helpfully answered through reference to the narrator's daughter, Lucy, who was born in Egypt and now clearly feels that Egypt is her home. Note what the narrator says when she talks about her daughter:
But then she was born here. And now she belongs. If I had taken her away then, when she was eight months old, she would have belonged with me.
Place and belonging are inextricably intertwined. Just as the narrator finds herself daydreaming about British rain and weather in response to her impossibly dry setting, thus revealing her identity as an English woman, so her daughter, because she was born in Egypt and grew up there, now "belongs," and the narrator can only ruefully reflect that she missed her opportunity of claiming her daughter for her own in England.
The net result of this on the narrator is that she finds herself in a position where she is literally stranded between two different worlds where there is no possibility of her ever being part of either. The final paragraph of the story makes this clear as it talks about the impossibility of the waves knowing anything of the sand of the desert, and the desert knowing anything of the depths of the sea. The narrator, just like the sandpiper, is stranded on the narrow patch of land where the sea and sand meet and is unable to belong now to either section. Her identity is defined through an inability to ascribe fully to either place, Egypt or England.