We present a new model for the generation of magnetic fields on large scales occurring at the end of cosmological reionisation. The inhomogeneous radiation provided by luminous sources and the fluctuations in the matter density field are the major ingredients of the model. More specifically, differential radiation pressure acting on ions and electrons gives rise to electric currents which induce magnetic fields on large scales. We show that on protogalactic scales, this process is highly efficient, leading to magnetic field amplitudes of the order of 10-11 Gauss. While remaining of negligible dynamical impact, those amplitudes are million times higher than those obtained in usual astrophysical magnetogenesis models. Finally, we derive the relation between the power spectrum of the generated field and the one of the matter density fluctuations. We show in particular that magnetic fields are preferably created on large (galactic or cluster) scales. Small scale magnetic fields are strongly disfavoured, which further makes the process we propose an ideal candidate to explain the origin of magnetic fields in large scale structures.