A search has been performed for photons originating in the decay of a neutral long-lived particle, exploiting the capabilities of the ATLAS electromagnetic calorimeter to make precise measurements of the flight direction of photons, as well as the calorimeter's excellent time resolution. The search has been made in the diphoton plus missing transverse energy final state, using the full data sample of 4.8 fb(-1) of 7 TeV proton-proton collisions collected in 2011 with the ATLAS detector at the LHC. No excess is observed above the background expected from Standard Model processes. The results are used to set exclusion limits in the context of gauge mediated supersymmetry breaking models, with the lightest neutralino being the next-to-lightest supersymmetric particle and decaying with a lifetime in excess of 0.25 ns into a photon and a gravitino.