We explore the evolution with redshift of the rest-frame colours and space densities of AGN hosts (relative to normal galaxies) to shed light on the dominant mechanism that triggers accretion onto supermassive black holes as a function of cosmic time. Data from serendipitous wide-area XMM surveys of the SDSS footprint (XMM/SDSS, Needles in the Haystack survey) are combined with Chandra deep observations in the AEGIS, GOODS-North and GOODS-South to compile uniformly selected samples of moderate luminosity X-ray AGN [L_X(2-10keV) = 1e41-1e44erg/s] at redshifts 0.1, 0.3 and 0.8. It is found that the fraction of AGN hosted by red versus blue galaxies does not change with redshift. Also, the X-ray luminosity density associated with either red or blue AGN hosts remains nearly constant since z=0.8. X-ray AGN represent a roughly fixed fraction of the space density of galaxies of given optical luminosity at all redshifts probed by our samples. In contrast the fraction of X-ray AGN among galaxies of a given stellar mass decreases with decreasing redshift. These findings suggest that the same process or combination of processes for fueling supermassive black holes are in operation in the last 5 Gyrs of cosmic time. The data are consistent with a picture in which the drop of the accretion power during that period (1dex since z=0.8) is related to the decline of the space density of available AGN hosts, as a result of the evolution of the specific star-formation rate of the overall galaxy population. Scenarios which attribute the evolution of moderate luminosity AGN since z approx 1 to changes in the suppermassive black hole accretion mode are not favored by our results.