Writing for Fact Magazine, Mark Fisher described the album's "delirial montage of funk, free jazz, Jamaican audio-mancy and the avant-garde" as "both carvernous and propulsive, ultra-abstract yet driven by dance music’s physical imperatives," and noted the "sonic alchemy" of Bovell's production work.Stylus Magazine called the album "a landmark of lunatic post-punk," writing that "these are political punk tunes deconstructed so that only the skeleton remains, and weaving between those bare bones are some of the nastiest sounds ever made." In 2004, Pitchfork Media ranked Y at number 35 on its list of the greatest albums of the 1970s, saying that "unlike most of the late-70s' no-wave types (and perennial imitators), The Pop Group were less concerned with eschewing convention than with vehemently eviscerating it."
The album has had a lasting impact, with artists such as the Minutemen, Primal Scream, Sonic Youth and Nick Cave citing the album as an influence on their work. Bassist Mike Watt commented that they "were making music that we were kind of inspired by and interested in" and that "they gave us permission to try to find what we were about. The Pop Group said “let’s take Funkadelic and put it with Beefheart. Why not?”"