  [Abridged] We assemble a sample of 45 intermediate X-ray luminosity galaxy
clusters at low redshifts using SDSS data to conduct a comprehensive
investigation into the photometric variation of red sequence modal galaxy
colours with environment. The clusters span a range of Bautz-Morgan types and
evolutionary stages and are representative of the global underlying
intermediate L_X cluster sample. We define cluster membership using SDSS
spectroscopic data and characterize the clusters by deriving new recession
velocities, velocity dispersions and other parameters for each. We construct
colour-magnitude diagrams for each of these clusters and obtain the position of
the red sequence using a robust line fitting algorithm with a Lorentzian merit
function. In doing so, we describe a population of discordant points on the
colour-magnitude plane which are the result of photometric blending, dust and
other causes. By fitting the clusters with Schechter functions to derive M*
values in each SDSS passband, we combine the red sequence of the galaxy
clusters together to form a composite sample. We detail how the modal colour
value of the red sequence varies with radius from the centre of this composite
cluster and local galaxy density for all SDSS colours. In agreement with
previous studies, these colours are shown to systematically move blueward with
increasing distance from the cluster centres, or equivalently lower local
galaxy density, whilst the width of the red sequence increases. This supports
the idea that the galaxies at the outskirts of these clusters have younger
luminosity-weighted ages than those at the core indicating their star formation
has been quenched more recently than in the core. A comparison of our derived
gradients in (g-r) with earlier works tentatively suggests that these gradients
vary with redshift which would reflect the hierarchical build-up of the red
sequence over time.
