A search for new phenomena has been performed in final states with at least one isolated high-momentum photon, jets and missing transverse momentum in proton–proton collisions at a centre-of-mass energy of s = 13 TeV. The data, collected by the ATLAS experiment at the CERN LHC, correspond to an integrated luminosity of 139 fb⁻¹. The experimental results are interpreted in a supersymmetric model in which pair-produced gluinos decay into neutralinos, which in turn decay into a gravitino, at least one photon, and jets. No significant deviations from the predictions of the Standard Model are observed. Upper limits are set on the visible cross section due to physics beyond the Standard Model, and lower limits are set on the masses of the gluinos and neutralinos, all at 95% confidence level. Visible cross sections greater than 0.022 fb are excluded and pair-produced gluinos with masses up to 2200 GeV are excluded for most of the NLSP masses investigated. [Figure not available: see fulltext.].