Wheat grain storage protein (GSP) content and composition are the main determinants of the end-use value of bread wheat (Triticum aestivum L.) grain. The accumulation of glutenins and gliadins, the two main classes of GSP in wheat, is believed to be mainly controlled at the transcriptional level through a network of transcription factors. This regulation network could lead to stable cross-environment allometric scaling relationships between the quantity of GSP classes/subunits and the total quantity of nitrogen per grain. This work conducted a genetic mapping study of GSP content and composition and allometric scaling parameters of grain N allocation using a bread wheat worldwide core collection grown in three environments. The core collection was genotyped with 873 markers for genome-wide association and 167 single nucleotide polymorphism markers in 51 candidate genes for candidate association. The candidate genes included 35 transcription factors (TFs) expressed in grain. This work identified 74 loci associated with 38 variables, of which 19 were candidate genes or were tightly linked with candidate genes. Besides structural GSP genes, several loci putatively trans-regulating GSP accumulation were identified. Seven candidate TFs, including four wheat orthologues of barley TFs that control hordein gene expression, were associated or in strong linkage disequilibrium with markers associated with the composition or quantity of glutenin or gliadin, or allometric grain N allocation parameters, confirming the importance of the transcriptional control of GSP accumulation. Genome-wide association results suggest that the genes regulating glutenin and gliadin compositions are mostly distinct from each other and operate differently.