The orientational order parameter of dense colloidal dispersions of plate-like particles as a function of volume fraction is measured using neutron diffraction. This non-invasive experimental approach directly provides the full particle orientation distribution from which the order parameters can be calculated. The orientation parameters are shown to be linked to the solids fractions of the cakes and the macroscopic permeability of the samples. However, this study suggests that, although orientation can be relevant for a given system, other factors can have a stronger influence, for example, the degree of dispersion or colloidal stability of the clay and may be the principle factor that controls permeability. In addition, we report enhanced ordering of these materials under the influence of an external cross-flow field.