We present deep Gemini Multi-Object Spectrograph South (GMOS-S)/Gemini optical broadband images for a complete sample of 46 southern 2 Jy radio galaxies at intermediate redshifts (0.05 <z <0.7). Based on them, we discuss the role of galaxy interactions in the triggering of powerful radio galaxies (PRGs). The high-quality observations presented here show for the first time that the overall majority of PRGs at intermediate redshifts (78-85 per cent) show peculiarities in their optical morphologies at relatively high levels of surface brightness (μV = 23.6 mag arcsec-2;ΔμV = [21,26] mag arcsec-2). The observed morphological peculiarities include tails, fans, bridges, shells, dust lanes, irregular features, amorphous haloes and multiple nuclei. While the results for many of the galaxies are consistent with them being observed at, or after, the time of coalescence of the nuclei in a galaxy merger, we find that more than one-third of the sample are observed in a pre-coalescence phase of the merger, or following a close encounter between galaxies that will not necessarily lead to a merger. By dividing the sample into Weak-Line Radio Galaxies (WLRGs; 11 objects) and Strong-Line Radio Galaxies (SLRGs; 35 objects) we find that only 27 per cent of the former show clear evidence for interactions in their optical morphologies, in contrast to the SLRGs, of which at least 94 per cent appear interacting. This is consistent with the idea that many WLRGs are fuelled/triggered by the Bondi accretion of hot gas. However, the evidence for interactions and dust features in a fraction of them indicates that the accretion of cold gas cannot always be ruled out. Of the 28 per cent of the sample that display evidence for significant starburst activity, we find that 92 per cent present disturbed morphologies, following the same general trend as the total and SLRG samples. By comparing our PRGs with various samples of quiescent ellipticals from the literature, we conclude that the percentage of morphological disturbance that we find here exceeds that found for quiescent ellipticals when similar surface brightnesses are considered. Overall, our study indicates that galaxy interactions are likely to play a key role in the triggering of active galactic nuclei (AGN)/jet activity.