We use the Fourth Data Release of the Sloan Digital Sky Survey to investigate the relation between galaxy rest frame u-r colour, morphology, as described by the concentration and Sersic indices, and environmental density, for a sample of 79,553 galaxies at z < ~0.1. We split the samples according to density and luminosity and recover the expected bimodal distribution in the colour-morphology plane, shown especially clearly by this subsampling. We quantify the bimodality by a sum of two Gaussians on the colour and morphology axes and show that, for the red/early-type population both colour and morphology do not change significantly as a function of density. For the blue/late-type population, with increasing density the colour becomes redder but the morphology again does not change significantly. Both populations become monotonically redder and of earlier type with increasing luminosity. There is no significant qualitative difference between the behaviour of the two morphological measures. We supplement the morphological sample with 13,655 galaxies assigned Hubble types by an artificial neural network. We find, however, that the resulting distribution is less well described by two Gaussians. Therefore, there are either more than two significant morphological populations, physical processes not seen in colour space, or the Hubble type, particularly the different subtypes of spirals Sa-Sd, has an irreducible fuzziness when related to environmental density. For each of the three measures of morphology, on removing the density relation due to it, we recover a strong residual relation in colour. However, on similarly removing the colour-density relation there is no evidence for a residual relation due to morphology. [Abridged]
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