Models of radio galaxy physics have been primarily based on high frequency ($\geqslant$1 GHz) observations of their jets, hotspots, and lobes. Without highly resolved low frequency observations, which provide information on older plasma, our understanding of the dynamics of radio galaxies and their interaction with their environment is limited. Here, we present the first sub-arcsecond (0.3") resolution images at 144 MHz of two powerful radio galaxies situated in rich cluster environments, namely 3C 34 and 3C 320, using the International Low Frequency Array Telescope. We detect for the first time at low frequencies a plethora of structures in these objects, including strikingly large filaments across the base of the lobes in both sources, which are spatially associated with dense regions in the ambient medium. For 3C 34 we report a spectral flattening in the region of the central filament, suggesting that the origin of the filaments is related to the presence of large-scale ordered magnetic fields. We also report periodic total intensity and spectral index banding of diffuse emission in the eastern lobe, seen for the first time in radio galaxy lobes. The hotspot complexes are resolved into multiple fragments of varying structure and spectral index; we discuss the implications for particle acceleration and jet termination models. We find at most smooth gradients in the spectral behaviour of the hotspot structure suggesting that particle acceleration, if present, may be occurring throughout the complex, in contrast to simple models, but different jet termination models may apply to both sources.