Spin magazine described the album's musical style as "[differing] from the crushed flowers studio formalisations of last year's Vauxhall and I, building instead on the earlier Your Arsenal, Morrissey's sly, unexpected blending of rockabilly and glam.

This version included a substantially altered running order, three previously unreleased tracks, "Honey, You Know Where to Find Me", "You Should Have Been Nice to Me" and "Fantastic Bird" (the last of which dates from the Your Arsenal sessions) as well as a single B-side "Nobody Loves Us".

[11] Q's Phil Sutcliffe wrote that Southpaw Grammar "shapes up as the kind of severe work that accrues more honour than love, more favourable comments than sales to record-buyers",[10] and the magazine later listed it as one of the top 50 albums of 1995.

"[3] Blender's Tony Power called it an "ugly, noisy, grumpy album, recorded while Britpop stole Moz's thunder and the Mike Joyce court case loomed.

"[5] Andrzej Lukowski of Drowned in Sound was more favourable in his retrospective assessment, writing that the album "is in some ways the most daring thing the ex-Smith has ever put his name to... [...] At the same time it's also pretty craven, in that it dilutes the impact of its three key tracks – 'The Teachers Are Afraid of the Pupils', 'The Operation' and 'Southpaw', dark, sprawling semi-instrumentals dominated by the remarkable drumming of Spencer James Cobrin – with lightweight fluff like 'Dagenham Dave' and 'The Boy Racer'.