We present the results of a study of the morphology of the dwarf galaxy population in Abell 868, a rich, intermediate-redshift (z = 0.154) cluster which has a galaxy luminosity function (LF) with a steep faint-end slope (α = -1.26 ± 0.05). A statistical background subtraction method is employed to study the B - R colour distribution of the cluster galaxies. This distribution suggests that the galaxies contributing to the faint-end of the measured cluster LF can be split into three populations: dwarf irregular galaxies (dIrrs) with B - R < 1.4; dwarf elliptical galaxies (dEs) with 1.4 ≤ B - K ≤ 2.5; and contaminating background giant ellipticals (gEs) with B - R > 2.5. The removal of the contribution of the background gEs from the counts only marginally lessens the faint-end slope (α = -1.22 ± 0.16). However, the removal of the contribution of the dIrrs from the counts produces a flat LF (α = -0.91 ± 0.16). The dEs and the dIrrs have similar spatial distributions within the cluster, except that the dIrrs appear to be totally absent within a central projected radius of about 0.2 Mpc (Ho = 75 km s-1 Mpc-1). The number densities of both dEs and dIrrs appear to fall off beyond a projected radius of ≃ 0.35 Mpc. We suggest that the dE and dIrr populations of A868 have been associated with the cluster for similar time-scales, but evolutionary processes such as 'galaxy harassment' tend to fade the dIrr galaxies while having a much smaller effect on the dE galaxies. The harassment would be expected to have the greatest effect on dwarfs residing in the central parts of the cluster.