[5] After the public and press interest garnered from Echo & the Bunnymen's debut album, Crocodiles, the band released the Shine So Hard EP which maintained their profile.

[8] In the liner notes to the 2003 remastered version of the album, lead singer Ian McCulloch said that he constantly had the American rock band the Velvet Underground's song "What Goes On" in the back of his mind.

[11] Melody Maker disagreed when in 1981 they said "the Bunnymen are continuing to play majestic, uplifting music that will shine through the dark days ahead of us".

[11] In the 2002 book Turquoise Days: The Weird World of Echo & the Bunnymen, author Chris Adams said that in 1995 McCulloch had said, "That spikey edge [of the album] still stands up.

"[13] In his 2005 book Rip It Up and Start Again: Post Punk 1978–1984, British music journalist Simon Reynolds described the sound of Heaven Up Here as having been filled out with "guitar overdubs, keyboard glints, vocal multitracking and atmospheric vapours".

[14] Comparing Heaven Up Here with Joy Division's 1980 album Closer, Reynolds said they are "harrowed by the same things [...] hypocrisy, distrust, betrayal, lost or frozen potential".

However, he said that "Closer shows Ian Curtis fatally mesmerized by his own dread visions, Heaven Up Here ultimately turns its face towards the light" with the tracks "No Dark Things" – which he describes as renouncing "death-wishful thinking" – and "All I Want" – which he describes as "a blasting celebration of desire for desire's sake" and "pure intransitive exhilaration".

He also stated that both Drummond and Rob Dickins, head of their record label Korova, hated the pictures from the shoot, and that he and Atkins had to fight for them to be used on the sleeve.

The release contained an expanded booklet written by music journalist Max Bell giving the background to the album.

In a 1982 interview with the band for the NME, rock journalist Barney Hoskyns described the album as "one of the most superior articulations of 'rock' form in living memory.

"[29] In his 1999 book From the Shores of Lake Placid and Other Stories, the band's manager Bill Drummond said "The album is dull as ditchwater.

"[31] Heaven Up Here sold well in the United Kingdom, staying on the UK Albums Chart for a total of 16 weeks and reaching a peak of number 10 in June 1981.

[34] The song "The Disease" was covered — re-titled as "From Heaven" — in 2024 by American industrial metal band Static-X for their album Project Regeneration Vol.