Guy Fletcher, John McCusker, Michael McGoldrick and Greg Leisz are shown to be part of the band.

[7][8] The album was followed by a standalone EP for Record Store Day called The Boy, containing four exclusive songs around a common theme of fairgrounds and boxing.

[9] Classic Rock writer David Quantick defined the album as one of the best of Knopfler's career, finding "gorgeous songs" which "sounds like it's lived a life that's full".

[11] AllMusic critic Timothy Monger gave the album a positive review, stating that Mark Knopfler's "output as a singer/songwriter has remained remarkably consistent and uniquely his own".

He went on to say that "Like its predecessor, 2018's Down the Road Wherever, One Deep River doesn't necessarily break new ground for Knopfler, but it does add a clutch of well-written, impeccably played songs to his canon ...