  We simulate the growth of galaxies and their central supermassive black holes
by implementing a suite of semi-analytic models on the output of the Millennium
Run, a very large simulation of the concordance LCDM cosmogony. Our procedures
follow the detailed assembly history of each object and are able to track the
evolution of all galaxies more massive than the Small Magellanic Cloud
throughout a volume comparable to that of large modern redshift surveys. In
this first paper we supplement previous treatments of the growth and activity
of central black holes with a new model for `radio' feedback from those AGN
that lie at the centre of a quasistatic X-ray emitting atmosphere in a galaxy
group or cluster. We show that for energetically and observationally plausible
parameters such a model can simultaneously explain: (i) the low observed mass
drop-out rate in cooling flows; (ii) the exponential cut-off at the bright end
of the galaxy luminosity function; and (iii) the fact that the most massive
galaxies tend to be bulge-dominated systems in clusters and to contain
systematically older stars than lower mass galaxies. This success occurs
because static hot atmospheres form only in the most massive structures, and
radio feedback (in contrast, for example, to supernova or starburst feedback)
can suppress further cooling and star formation without itself requiring star
formation. We discuss possible physical models which might explain the
accretion rate scalings required for our phenomenological `radio mode' model to
be successful.
