We study the colour-magnitude relation (CMR) for a sample of 172 morphologically-classified E/S0 cluster galaxies from the ESO Distant Cluster Survey (EDisCS) at 0.4<z<0.8. The intrinsic colour scatter about the CMR is very small (0.076) in rest-frame U-V. Only 7% of the galaxies are significantly bluer than the CMR. The scarcity of blue S0s indicates that, if they are the descendants of spirals, these were already red when they became S0s. We observe no dependence of the CMR scatter with redshift or cluster velocity dispersion. This implies that by the time cluster E/S0s achieve their morphology, the vast majority have already joined the red sequence. We estimate the galaxy formation redshift z_F for each cluster and find that it does not depend on the cluster velocity dispersion. However, z_F increases weakly with cluster redshift. This trend becomes clearer when including higher-z clusters from the literature, suggesting that, at any given z, in order to have a population of fully-formed E and S0s they needed to have formed most of their stars 2-4 Gyr prior to observation. In other words, the galaxies that already have early-type (ET) morphologies also have reasonably-old stellar populations. This is partly a manifestation of the progenitor bias, but also a consequence of the fact that the vast majority of the ETs in clusters (in particular the massive ones) were already red by the time they achieved their morphology. E and S0 galaxies exhibit very similar colour scatter, implying similar stellar population ages. We also find that fainter ETs finished forming their stars later, consistent with the cluster red sequence being built over time and the brightest galaxies reaching the red sequence earlier than fainter ones. Finally, we find that the ET cluster galaxies must have had their star formation truncated over an extended period of at least 1 Gyr. [abridged]
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