The results of analysis of HST I-band imaging of a sample of 41 radio galaxies spanning three orders of magnitude in radio luminosity at redshift z~= 0.5 are presented. These results represent the first stage in a coordinated programme to study the connection between radio luminosity and host galaxy properties, black hole masses and cluster environments in radio galaxies spanning a wide range in radio luminosity over a restricted range in redshift. The full sample is comprised of objects drawn from four complete, low-frequency selected radio samples with progressively fainter flux-density limits (3CRR, 6CE, 7CRS and the new TexOx-1000 sample). Modelling of the HST imaging data shows that the host galaxies have surface-brightness distributions consistent with those expected for classic ellipticals (Sérsic parameter, β~= 0.25), with β in the range 0.17 <β <0.30, and a mean of = 0.23 +/- 0.01. The luminosities of the host galaxies are found to be comparable with those of galaxies drawn from the bright end of the local cluster galaxy luminosity function, spanning the range 0.7L* <L <10 L*, with a mean of 3.2 +/- 0.3L*, after correcting for the effects of passive evolution. In addition, the radio galaxies are shown to follow a Kormendy (μe-re) relation indistinguishable from that of both powerful low-redshift radio galaxies and local Abell brightest cluster galaxies (BCGs). Combining our new results with those in the literature it is found that the scalelengths and Kormendy relations of 3C-class radio galaxies do not vary significantly over the redshift range 0.0 <z <0.8, providing no evidence for dynamical evolution of this class of host galaxy within this redshift interval. Converting the host galaxy luminosities into black hole mass estimates, using the local Mbh-Mbulge correlation, predicts that the radio galaxies harbour central black holes with masses in the range 108.1 Msolar <Mbh < 109.5 Msolar, with a geometric mean of = 108.87+/-0.04 Msolar. Finally, a significant (~= 3σ) correlation is found between black hole mass and 151-MHz radio luminosity for those objects in the sample with either high-excitation nuclear spectra or classical double radio structures.