[3] The tour had been notable for its debauchery; Ian Dury's "Sex & Drugs & Rock & Roll" served as the setlist's official closing song.

[7]The song was recorded quickly; bassist Bruce Thomas recalled, "We literally did the best tracks on [This Year's Model]—"Pump It Up", "Chelsea"—in one afternoon.

The song features a prominent organ performance by Steve Nieve that was described by Ryan Prado of Paste as "like a carnival train headed off the rails".

[12] Bassist Bruce Thomas said of his part, "When I analyzed it, it was actually a hybrid of a riff from the Everly Brothers song called "The Price of Love".

[19] Costello recalled the video as "cheaply produced" and noted the director's use of a fisheye lens that made him look "bug-eyed".

... My bizarre attempts at rug-cutting in the "Pump It Up" video were becoming as much a calling card as a comedian's catchphrase, and I could sense myself being vacuumed up into the dust bag of light entertainment.

[21]The video for "(I Don't Want to Go to) Chelsea" was shot the same day in London, and all the musicians can be seen wearing the same clothes, although drummer Pete Thomas sports a plain grey jacket for "Pump It Up".

Bassist Bruce Thomas had cut his right hand on a bottle a few weeks previously and had needed eight stitches; his bandage can be clearly seen in both videos.

AllMusic's Deming calls the song "as exciting, insistent, and physically powerful as anything Costello might have been railing against" and noted that the track "perfectly captures the giddy but terrifying feeling of a wild, adrenaline-fueled all-night party that's dangling on the verge of collapse".

[4] Amy Poulter of The Virginian Pilot writes, "Even if you're not a fan, you've most likely heard the song and gotten caught up in its infectiously-peppy rhythm and melody".

Jim Beviglia of American Songwriter named it Costello's 20th best song, calling it "a true tour de force for bassist Bruce Thomas" and stating, "When Thomas joins up with Costello on guitar and Steve Nieve on organ for that thundering riff, it's one of those great rock moments, the power of which you can never properly explain to someone without saying, 'Here, listen to this'".

[12] In a list for Louder, David Ford named the song one of Costello's top ten best, calling it "a glorious piece of sweaty pop' and "a brilliantly constructed record".

[31] Olivia Rodrigo's 2021 song "Brutal" features a guitar riff similar to that of "Pump It Up", leading to accusations of plagiarism.

[32][33][34] In response, Costello—who cited Bob Dylan's "Subterranean Homesick Blues" as inspiration for "Pump It Up"—commented, "This is fine by me ...