The diffuse intracluster light (ICL) contains a significant fraction of the total stellar mass in clusters of galaxies, and contributes in roughly equal proportion as the hot intracluster medium to the total baryon content of clusters. Because of the potential importance of understanding the origin of the ICL in the context of the formation and evolution of structure in the Universe, the field has recently undergone a revival both in the quality and quantity of observational and theoretical investigations. Because of cosmological dimming, the observational work has mostly concentrated on low-redshift clusters, but clearly observations at higher redshifts can provide interesting clues about the evolution of the diffuse component. In this paper we present the first results of a programme to characterize the ICL of intermediate-redshift clusters. We find that at z similar to 0.3, the X-ray cluster RXJ0054.0-2823 already has a significant ICL and that the fraction of the total light in the ICL and the brightest cluster galaxy (BCG) is comparable to that of similar clusters at lower redshift. We also find that the kinematics of the ICL is consistent with it being the remnant of tidally destroyed galaxies streaming in the central regions of the cluster, which has three central giant elliptical galaxies acting as an efficient 'galaxy grinding machine'. Our cluster has a bi-modal radial velocity distribution and thus two possible values for the velocity dispersion. We find that the cluster fits well in the correlation between BCG+ICL fraction and cluster mass for a range of velocity dispersions, leading us to question the validity of a relevant correlation between these two quantities.