[3] A 180g vinyl reissue, remastered from the original ¼” tapes and cut half-speed at Abbey Road Studios by Miles Showell, was released in December 2018.

Reviewer Mark Cooper hailed "Martin McCarrick's accordion that pokes its way into Peek A Boo ... a carny piece of musical imagination".

He noted that "the rest of the record bursts with similar acts of imagination", saying: "full honours go to the aforementioned McCarrick for all manner of shrewd decorations and drummer Budgie for endlessly inventive rhythm work that manages to pinpoint the tension inherent in each song without ever lapsing into an obvious beat".

[8] Melody Maker highly praised its first single, "Peek-a-Boo", and called it "quite the most astounding British record" of 1988, and "a brightly unexpected mixture of black steel and pop disturbance.

"[11] Record Mirror also particularly enjoyed that song when reviewing the album: "The highlight is the restrained 'The Last Beat of My Heart', where Siouxsie's voice explores new ground as she caresses a haunting melody."

Discussing "Peek-a-Boo", critic Tony Fletcher said that its "mood fell in perfectly with their beloved London's summer fascination with the sparsity and confusion that call Acid House, Psychedelic and how!"

He described the music of "Peek-a-Boo" as "a crazed assortment of fairground accordions, abrupt horns, distant to-and-fro vocals-exotic, erotic, a dancefloor winner for sure and all of three minutes short.

"[13] Fletcher also hailed the other tracks, noting "an almost lilting reggae feel to the beginning of "Killing Jar", a fragile, waif-like Siouxsie backed only by translucent guitar and a keyboard bass on the brief "Rawhead and Bloodybones", and a delightful, majestic ballad the likes of which it had been a safe assumption was beyond their reach on "The Last Beat of My Heart".

Reviewer Parke Puterbaugh wrote that the record was "a fascinating plunge into the subconscious" and was "Dream-like" and "hypnotic", further emphasizing, "Peepshow brims with nonlinear logic, compulsive rhythms, and icy, crystalline textures."