Inclusive jet differential cross sections for the reaction e+p → e+ + jet + X with quasi-real photons have been measured with the ZEUS detector at HERA. These cross sections are given for the photon-proton centre-of-mass energy interval 134 < W < 277 GeV and jet pseudorapidity in the range -1 < ηjet < 2 in the laboratory frame. The results are presented for three cone radii in the η - φ plane, R = 1.0, 0.7 and 0.5. Measurements of dσ/dηjet above various jet-transverse-energy thresholds up to 25 GeV and in three ranges of W are presented and compared to next-to-leading order (NLO) QCD calculations. For jets defined with R = 1.0 differences between data and NLO calculations are seen at high ηjet and low EjetT. The measured cross sections for jets defined with R = 0.7 are well described by the calculations in the entire measured range ηjet and EjetT. The inclusive jet cross section for EjetT > 21 GeV is consistent with an approximately linear variation with the cone radius R in the range between 0.5 and 1.0, and with NLO calculations.