Steven Edelstone of Paste said, "It sounds like the band held a competition during quarantine last year to write the prettiest songs they possibly could, ranked the 10 most beautiful ones they came up with and packaged them into a single record ... And the results are stunning.

"[11] Johnny Sharp of Uncut stated that there was "a gorgeously somnambulant yet softly romantic feel to these 10 songs" and that they benefitted from the "masterfully subtle arrangement touches".

[12] In Mojo, Victoria Segal said that the band had gone "back into a gentler bubble" following the bleakness of previous album Giants of All Sizes, and that "Garvey's lyricism is elevated by the subtle complexity of the music, clarinets, choral voices and churchy keyboards whispering through the vents of these songs, causing a quiet stir".

[7] Phil Mongredien of The Observer stated that "With the exception of impassioned closer 'What Am I Without You', there is nothing on Flying Dream 1 that leaps out at the listener; instead these songs represent subtle gradations of softly articulated warmth and empathy."

He ended his review saying, "Flying Dream 1 may be devoid of gnarly anthems like 'Grounds For Divorce' or grandiose moments like 'One Day Like This', but the record's unhurried approach and unassuming manner will still bring comfort to those who seek solace in Garvey's lyrics and Elbow's adept consistency.