If you mean specifically the Cealdhame segment, it was mostly influenced by the two semesters I studied Old English.
If you mean the whole fourth section, the influences aren’t really fantasy fiction exactly. One room resembles a scene from House more than anything else, one room is supposed to be a Neruda poem/Waterhouse painting, one room is the film The Nightmare Before Christmas. In general I think the surrealism and “collage” sensibility of the fourth section ultimately derive from Space Ghost Coast to Coast.
The fantasy books that influence me the most, where “influence” is defined as realizing where I got an idea that I had thought was original, are the Chronicles of Narnia and Madeleine L’Engle’s books. In particular L’Engle’s perspective and ideas are kind of baked into my brain as baseline generic fantasy.
Fantasy fiction I really dig and aspire to includes the Dirk Gently books, what I remember of the Gormenghast books, the Sandman comics, the League of Extraordinary Gentlemen comics, the Doctor McNinja comics, Jesse Moynihan’s Forming comic, Evan Dahm’s Rice Boy/Order of Tales/Vattu comics, the show called Adventure Time, and let’s say Venture Bros. counts as fantasy. But this all influences stuff like the Little Match Girl games more than A Rope of Chalk. I guess that one room in A Rope of Chalk is very Sandmanesque, though.