Not Too Far Away was reviewed by AllMusics Timothy Monger wherein he gave the album four out of five stars while David Schuster from ON Magazine gave the album a rating of nine out of ten.
AllMusic reviewer Timothy Monger noted Armatrading's "heartfelt melodies", "quality songs" and "smartly crafted [...] pop" and praised her "consistent creative expression", giving special mention to the tracks "I Like It When We're Together" and "This Is Not That". He concluded by giving the album four out of five stars, calling Armatrading's achievements "genuinely impressive". ON Magazine's David Schuster called Not Too Far Away "an astonishing album, with beautifully written songs", and "exquisite". He gave the album nine out of ten and suggested that, following this album, Armatrading should be considered for a Brit Awards Lifetime Achievement Award. 
