We present deep GMOS-S/Gemini optical broad-band images for a complete sample of 46 southern 2Jy 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 % ) show peculiarities in their optical morphologies at relatively high levels of surface brightness ( \tilde { \mu } _ { V } = 23.6 ~ { } mag~ { } arcsec ^ { -2 } ; \Delta \mu _ { V } \simeq [ 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 % of the former show clear evidence for interactions in their optical morphologies , in contrast to the SLRGs , of which at least 94 % appear interacting . This is consistent with the idea that many WLRGs are fuelled/triggered by 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 can not always be ruled out . Of the 28 % of the sample that display evidence for significant starburst activity , we find that 92 % 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 AGN/jet activity .