In his review for AllMusic, Tom Demalon called the album "a low-key, joyous run-through of mostly traditional, blues-based songs with a handful of originals."[1] Demalon continued:
Despite the high-profile presence of Knopfler, the Notting Hillbillies succeed in sounding like a band with Knopfler often taking a backseat to his bandmates, although he does sing lead on the lovely "Your Own Sweet Way". The styles range from the gorgeous harmonies of "Railroad Worksong" with some mournful guitar from Knopfler, to the '50s-style rock ballad "Bewildered", to the breezy, tropical-flavored "One Way Gal".[1]
Demalon concluded that Missing...Presumed Having a Good Time is a "delightful record that doesn't overstay its welcome."[1]
The song "Lonesome Wind Blues" is a non-album track that appears on two different European/UK CD & 12" singles: "Will You Miss Me" and "Feel Like Going Home".