Galaxy interactions are thought to be one of the main triggers of active galactic nuclei (AGN), especially at high luminosities, where the accreted gas mass during the AGN lifetime is substantial. Evidence for a connection between mergers and AGN, however, remains mixed. Possible triggering mechanisms remain particularly poorly understood for luminous AGN, which are thought to require triggering by major mergers, rather than secular processes. We analyse the host galaxies of a sample of 20 optically and X-ray selected luminous AGN (log(Lbol [erg s−1]) > 45) at z ∼ 0.6 using Hubble Space Telescope Wide Field Camera 3 data in the F160W/H band. 15/20 sources have resolved host galaxies. We create a control sample of mock AGN by matching the AGN host galaxies to a control sample of non-AGN galaxies. Visual signs of disturbances are found in about 25 per cent of sources in both the AGN hosts and control galaxies. Using both visual classification and quantitative morphology measures, we show that the levels of disturbance are not enhanced when compared to a matched control sample. We find no signs that major mergers play a dominant role in triggering AGN at high luminosities, suggesting that minor mergers and secular processes dominate AGN triggering up to the highest AGN luminosities. The upper limit on the enhanced fraction of major mergers is ≤20 per cent. While major mergers might increase the incidence of luminous AGN, they are not the prevalent triggering mechanism in the population of unobscured AGN.