Following the release of the band's sixth album, Waiting for the Moon in 2003, Tindersticks had entered an extended hiatus before reconvening to perform at the Don't Look Back event in September 2006.

The remaining members of Tindersticks felt reinvigorated by the performance, and relocated to France to begin working on new material in the summer of 2007, recording and producing the album at their own Le Chien Chanceaux studio in Limousin.

[1] The remaining three members, Staples, guitarist Neil Fraser, and multi-instrumentalist David Boulter, felt reinvigorated by the concert and were keen to continue as Tindersticks.

Dan McKinna and Thomas Belhom, who later became full-time members of the group, were recruited to play bass and drums respectively, and long-time collaborators Ian Caple, Terry Edwards, Lucy Wilkins and Calina de la Mare helped with the recording and the arrangements.

"[10] PopMatters remarked that "ornamental instrumentation is used quite sparingly",[6] while other critics noted the "smoky, solitary atmosphere and muted string arrangements"[8] and "restrained" brass accompaniment.

"[12] Dusted magazine also commended the arrangements, remarking that they carried "poignant depth, cinematic sweep and enviable perfectionism",[7] while Drowned in Sound described them as "immaculate".

[13] The pace of The Hungry Saw's music was described by Uncut as "funereal",[14] while Tiny Mix Tapes remarked upon the album's "low-down grooves" and "slow tempos".

[12] Despite the "heavily maudlin"[10] sound of the album, "The Flicker of a Little Girl" was described as a "sprightly",[11] "breezy piano-rolled folk lullaby"[8] that "owes a debt to Lee Hazlewood.

[15][17][18] The "almost poppy"[12] song "Boobar Come Back to Me", which employs a call and response vocal pattern,[6][8] was described as "one of The Hungry Saw's undisputed highlights"[18] that "suggests another solitary Staples serenade about lost love, before slowly blossoming into a wonderful Spectorized finale.

[23] After performing at some music festivals in the summer of 2008, more European dates followed in November and December,[24] before Tindersticks undertook a tour of North America in February and March 2009.

[16] Drowned in Sound's Billy Hamilton offered the opinion that while "there's very little here that couldn't slot seamlessly into any of the group's output", The Hungry Saw was "something that can be unequivocally relied upon to produce the goods.