A search is performed for localised excesses in dijet mass distributions of low-dijet-mass events produced in association with a high transverse energy photon. The search uses up to 79.8 fb$^{-1}$ of LHC proton-proton collisions collected by the ATLAS experiment at a centre-of-mass energy of 13 TeV during 2015-2017. Two variants are presented: one which makes no jet flavour requirements and one which requires both jets to be tagged as $b$-jets. The observed mass distributions are consistent with multi-jet processes in the Standard Model. The data are used to set upper limits on the production cross-section for a benchmark $Z^\prime$ model and, separately, on generic Gaussian-shape contributions to the mass distributions, extending the current ATLAS constraints on dijet resonances to the mass range between 225 and 1100 GeV.