[en] Inclusive jet differential cross sections for the reaction ep→jet+X at Q² below 4 GeV² have been measured with the ZEUS detector at HERA using an integrated luminosity of 0.55 pb^-1. These cross sections are given in the kinematic region 0.2< y<0.85, for jet pseudorapidities in the ep-laboratory range -1<η^jet<2 and refer to jets at the handron level with a cone radius of one unit in the η-φ plane. These results correspond to quasi-real photoproduction at centre-of-mass energies in the range 130-270 GeV and, approximately, for jet pseudorapidities in the interval -3<η^jet(γp CMS)<0. These measurements cover a new kinematic regime of the partonic structure of the photon, at typical scales up to ∝300 GeV² and photon fractional momenta down to x_γ∝10^-2. Leading logarithm parton shower Monte Carlo calculations, which include both resolved and direct processes and use the predictions of currently available parametrisations of the photon parton distributions, describe in general the shape and magnitude of the measured η^jet and E_T^jet distributions. (orig.)