Understanding the evolution of accretion activity is fundamental to our understanding of how galaxies form and evolve over the history of the Universe. We analyse a complete sample of 27 radio galaxies which includes both high-excitation (HEGs) and low excitation galaxies (LEGs), spanning a narrow redshift range of 0.9 < z < 1.1 and covering a factor of ~1000 in radio luminosity. Using data from the Spitzer Space Telescope combined with ground-based optical and near-infrared imaging, we show that the host galaxies have masses in the range of 10.7 < log (M /M_sun) < 12.0 with HEGs and LEGs exhibiting no difference in their mass distributions. We also find that HEGs accrete at significantly higher rates than LEGs, with the HEG/LEG division lying at an Eddington ratio of ~0.04, which is in excellent agreement with theoretical predictions of where the accretion rate becomes radiatively inefficient, thus supporting the idea of HEGs and LEGs being powered by different modes of accretion. Our study also shows that at least up to L_151MHz ~3x10^27 W /Hz /sr, HEGs and LEGs are indistinguishable in terms of their radio properties. From this result we infer that, at least for the lower radio luminosity range, another factor besides accretion rate must play an important role in the process of triggering jet activity.