Hubble Space Telescope R-band images of a sample of 10 radio galaxies (RG), 10 radio-loud quasars (RLQ) and 13 radio-quiet quasars (RQQ) at redshift z 0.2 are presented. The sources comprising the radio-loud sub-samples have been selected to be indistinguishable in the P_5GHz - z plane. The two quasar sub-samples have been similarly selected to have indistinguishable distributions in the V - z plane. All three sub-samples have been analysed with two-dimensional modelling software, designed to accurately determine the host-galaxy parameters. The modelling results show all of the RG, and all of the quasars with M_V < -23, to have bulge-dominated host galaxies, excluding the hypothesis that host morphology is responsible for the radio-loudness dichotomy. Furthermore, the host galaxies are found to be essentially identical to a de Vaucouleurs (b = 0.25) law, with 30/33 objets having b parameters in the range 0.2 < b < 0.3. The hosts of all of the objects studied are found to be extremely luminous (L ³ L_*), with 25/33 objects having L ³ 2L_*. The hosts of the RQQs are found to be typically 0.4 magnitudes fainter than their radio-loud counterparts. The host galaxies of all three sub-samples are found to be larger than average ellipticals (< r_e > = 10.5 kpc), with a trend found for the RQQ hosts to be some 20% smaller than those of the RLQs. For the first time it is demonstrated that the hosts of quasars, as well as RG, display a Kormendy relation basically identical to that of inactive ellipticals. In conclusion with the previous K-band modelling of this sample (Taylor et al. 1996) the first set of reliable optical-infrared colours for a significant sample of AGN host galaxies has been determined. The R - K colours of the hosts in all three sub-samples are shown to be consistent with each other, with the close agreement of the median colour of R - K=2.5 with that expected from a ~ 14 Gyr-old stellar population implying that the host galaxies of both RG and quasars are consistent with having formed at high redshift (z ³ 3). The nuclear colours of the RGs are shown to be perfectly consistent with those of dust reddened RLQ nuclei. The combined luminosity, scalelength, Kormendy relation and R - K colour results for the RG and RLQ sub-samples clearly demonstrate that they are drawn from the same parent population, in strong support of the orientation-based unification scheme of Barthel (1989). The corresponding results for the full 33 objects sample show that, in terms of their global structural parameters, the hosts of powerful AGN are no different to normal massive ellipticals.