  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]
