After a prolonged delay in which an entire album's worth of work was scrapped, the Blue Nile released Hats to rave reviews, including a rare five-star rating from Q magazine.

Like the Blue Nile, It's Immaterial also ran into difficulties making their record, overrunning their allotted time and eventually spending a year at Castlesound.

"[6] In a 2012 interview with ClashMusic.com, Buchanan reflected on the time lost trying to make the album: "We pretty much put the record [A Walk Across the Rooftops] out, promoted it and then the next thing we knew we were back in the studio.

As a promotional tool, A&M Records—who distributed Hats in North America—took out a full-page advertisement in Billboard magazine offering a free copy of the CD to anyone who called a toll-free number which was provided.

The remastering process was overseen by original engineer Calum Malcolm, along with Paul Buchanan and Robert Bell, who chose the songs for the bonus CD.

Describing the album as "absolutely superb", David Cavanagh of Sounds found that Hats differed significantly from A Walk Across the Rooftops in both its recording technology and aspired moods.

[19] Johnny Black of Q noted the more stripped-down nature of the album's songs and praised the band's new direction, stating that "if Hats has a flaw, it's only that it's too perfect, too considered.

"[16] NME's David Quantick felt that the album demonstrated the band's flair for writing "incredibly simple-sounding, emotional records about the stuff that fascinates them.

"[14] Simon Reynolds, writing in Melody Maker, stated that "only the laziest ear would confuse this crystalline perfection with the hygiene and polish of plastic pop" and described the album as "big music, that leaves you feeling very small, very still and very close to tears.

"[21] In a more lukewarm assessment, David Thigpen of Rolling Stone complimented the band's use of instrumentation to convey emotions, but felt that Paul Buchanan's singing range was limited and the album occasionally veers "into sticky melancholy.

"[11] Following the release of the album's 2012 remastered version, D. M. Edwards of PopMatters wrote that Hats sounded "richer, fuller, more layered and produced" than A Walk Across the Rooftops and provided a "pretty unrelenting opportunity to really wallow in gorgeous, sublime, melancholy.

[30] In 2024, in the opening and closing lyrics to her song "Guilty as Sin" from the album The Tortured Poets Department, Taylor Swift included a reference to a person sending her "The Downtown Lights" to listen to.