High-resolution N-body re-simulations of 15 massive (10 14 10 15 M⊙) dark matter haloes have been combined with the hybrid galaxy formation model GalICS (Hatton et al. 2003), to study the formation and evolution of galaxies in clusters, within the framework of the hierarchical merging scenario. This paper describes the high-resolution resimulation technique used to build the dark matter halo sample, and discusses its reliability. New features incorporated in GalICS include a better description of galaxy positioning after dark matter halo merger events, a more reliable computation of the temperature of the inter-galactic medium as a function of redshift, that also takes into account the re ionisation history of the Universe, and a semi-analytic description of the ram pressure strippi ng of cold gas from galactic discs, suffered by galaxies during their motion through the diffuse hot intra-cluster medium. Within the multitude of available model results, we choose to focus here on the luminosity functions, morphological fractions and colour distributions of galax ies in clusters and in cluster outskirts, at z = 0. No systematic dependency on cluster richness is found either for the galaxy luminosity functions, morphological mixes, or colour distributions. Moving from higher density (cluster cores), to lower density environments (clust er outskirts), we detect a progressive flattening of the luminosity functions, an increase of the fr action of spirals and a decrease of that of ellipticals and S0s, and the progressive emergence of a bluer tail in the distributions of galaxy colours, especially for spirals. As compared to cluster spirals, early-type galaxies show a flatter luminosity function, and more homogeneous and redder colours. An overall good agreement is found between our results and the observations, particularly in terms of the cluster luminosity functions and morphological mixes. However, some discrepancies are also apparent, with too faint magnitudes of the brightest cl uster members, especially in the B band, and galaxy colours tendentially too red (or not blue enough) in the model, with respect to the observations. Finally, ram pressure stripping appea rs to affect very little our results.