Like the band's prior EPs and singles, most of the songs on this album are bathed in heavy layers of delay (echo) and reverb, used on both the guitars and the vocals, to give a disorientingly psychedelic overall effect. The lyrics of "Butterfly" pertain directly to the so-called butterfly effect, and the song "Catching the Butterfly," from the band's 1997 album Urban Hymns, is apparently a continuation of this theme. Guitarist Nick McCabe has stated that the track was recorded at 3:00 a.m. while playing along with a Steely Dan sample. The album's closing song, "See You in the Next One (Have a Good Time)", is built on a subdued piano motif played by McCabe and atmospheric acoustic guitars played by vocalist Richard Ashcroft. After this album, the band's music moved in a less psychedelic, more structured direction, and their name was officially changed to "The Verve" for legal reasons, so as not to clash with the record label Verve Records.
As with all of the band's releases, A Storm in Heaven features enigmatic artwork designed by Brian Cannon. The cover photo was shot inside Thor's Cave in Staffordshire, England. The vinyl LP version came in gatefold packaging.
In a reappraisal of the album, Delusions of Adequacy notes that A Storm in Heaven transcended the other albums of its time:
A highly burnished synthesis of the warbling hard rock of the Doors, the infinite rhythmic groove of Can, the space-fried improvisations of Yeti-era Amon Düül II, and the effects-pedal anchor of My Bloody Valentine, A Storm in Heaven may well have been the best neo-psychedelic album released in the 1990s. While often clumped together with the other English bands leading the shoegaze movement during the same time period, the Verve was creating a far different version of the thick atmospherics the genre became known for. Despite some minor cosmetic similarities, Loveless this was not. In fact, I’d go so far as to say that guitarist Nick McCabe gazed shoe-ward with far better results than Kevin Shields ever did. While Loveless remained firmly anchored to the early-90s British scene, A Storm in Heaven flew figure eights somewhere over its head.