We present deep Gemini Multi-Object Spectrograph-South optical broad-band images for a complete sample of 20 Sloan Digital Sky Survey selected type II quasars taken from Zakamska et al., with redshifts in the range 0.3 < z < 0.41 and [O III]λ5007 emission-line luminosities L[O iii ]>108.5 L. The images were taken with the aim of investigating the interaction status of the quasar host galaxies, in order to determine the significance of galaxy interactions in triggering nuclear activity. We find that 15 of our sample of 20 (75 per cent) show evidence for interaction in the form of tails, shells, fans, irregular features, amorphous haloes and double nuclei. The median surface brightness of the features is μ˜r corr =23.4 mag arcsec-2 and the range is Δμr corr ≃[20.9,24.7] mag arcsec-2. We find a similar rate of interaction signatures in the type II quasars as in a comparison sample of quiescent early-type galaxies at similar redshift (67 per cent) taken from Ramos Almeida et al. (RA11). However the surface brightness of the detected features is up to 2 mag brighter for the type II quasars than for the quiescent early types, which have surface brightnesses in the range Δμr corr ≃[22.1,26.1] mag arcsec-2 and a median surface brightness μ˜r corr =24.3 mag arcsec-2. Despite the relatively small sample size, this may indicate that the mergers witnessed in the comparison sample galaxies could have different progenitors, or we may be viewing the interactions at different stages. We also compare our results with those of Ramos Almeida et al. (RA12) who made a similar analysis using a complete sample of radio-loud active galactic nuclei (AGN). They find a higher rate of interaction signatures in the radio-loud AGN (95 per cent) than the type II quasars, but a very similar range of surface brightnesses for the morphological features Δμr corr ≃[20.9,24.8] mag arcsec-2, possibly indicating a similarity in the types of triggering interactions. The wide range of features detected in the type II quasar sample suggests that AGN activity can be triggered before, during or after the coalescence of the black holes, with six of the 20 objects (30 per cent) having double nuclei. Overall, the results presented here are consistent with the idea that galaxy interaction plays an important role in the triggering of quasar activity. We also use time-scale arguments to show that it is unlikely that most radio-quiet quasars cycle through a radio-loud phase as part of a single quasar triggering event.