This is a track from the self-titled debut album by Anna Calvi. The English/Italian singer-songwriter has a cinematic vision for her songs ensuring she pays close attention to their arrangements. In an interview with NPR she explained that for this track's instrumentation, "I wanted to have a melodic motif that just keeps building and building, and it's kind of like a metaphor for desire. So you hear it on the harmonium, and then you hear it in the guitar, the same melodic refrain, and it just grows throughout the song as the desire grows stronger. This melody is heard in more and more instruments until at the end, it's almost just bursting. For me, it's really important that the music is telling you half the story; it's telling you as much about what the song is about as the lyrics are."
English musician and producer Brian Eno sung backing vocals on both "Desire" and another Anna Calvi track, "Suzanne and I." Calvi recalled to Artrocker: "He's funny when he sings because he'll sit down and read a book while he's doing the backing vocals, at the same time (laughs). I actually met him through a friend of his, he had come to my gig and then told Brian about me and he then contacted my management and we went for lunch. He's really into gospel music."