CERN-LHC. Measurement of the inclusive production of isolated prompt photons in proton-proton collisions at a centre-of-mass energy of 7 TeV. The data sample used has an integrated luminosity of 35 pb-1. Photons are isolated if the total transverse energy in a cone (in phi,eta space) of radius R=0.4 is less than a cut value of 4 GeV. The four systematic errors shown in the tables represent, respectively, the uncertainties in (1) the purity measurment, (2) the photon selection and identification efficiency, (3) the correlation between the efficiency and purity determination and (4) the unfolding process. The luminosity uncertainty of 3.4% is shown separately. Note added (27 JUN 2014): The cross section values reported in Tables 1-4 below should be multiplied by a factor of 1.0187 to take into account the updated value of the integrated luminosity for the ATLAS 2010 data taking period. The uncertainty on the global normalisation ("Lumi") increases slightly from 3.4% to 3.5%. See Eur.Phys.J. C73 (2013) 2518 for more details.