We explore the evolution with redshift of the rest-frame colours and space densities of active galactic nuclei (AGN) hosts (relative to normal galaxies) to shed light on the dominant mechanism that triggers accretion on to supermassive black holes as a function of cosmic time. Data from serendipitous wide-area XMM surveys of the Sloan Digital Sky Survey (SDSS) footprint (XMM/SDSS; Needles in the Haystack Survey) are combined with Chandra deep observations in the All-wavelength Extended Groth Strip International Survey (AEGIS), GOODS-North and GOODS-South to compile uniformly selected samples of moderate-luminosity X-ray AGN [LX(2–10 keV) = 1041–1044 erg s−1] 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 fuelling supermassive black holes is in operation in the last 5 Gyr of cosmic time. The data are consistent with a picture in which the drop of the accretion power during that period (1 dex 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≈ 1 to changes in the suppermassive black hole accretion mode are not favoured by our results.