A search for diphoton events with large missing transverse momentum has been performed using proton-proton collision data at sqrt(s) = 7 TeV recorded with the ATLAS detector, corresponding to an integrated luminosity of 4.8 fb^-1. No excess of events was observed above the Standard Model prediction and model-dependent 95% confidence level exclusion limits are set. In the context of a generalised model of gauge-mediated supersymmetry breaking with a bino-like lightest neutralino of mass above 50 GeV, gluinos (squarks) below 1.07 TeV (0.87 TeV) are excluded, while a breaking scale Lambda below 196 TeV is excluded for a minimal model of gauge-mediated supersymmetry breaking. For a specific model with one universal extra dimension, compactification scales 1/R <1.40 TeV are excluded. These limits provide the most stringent tests of these models to date.