Determinations of the UV luminosity function of AGN at high redshifts are important for constraining the AGN contribution to reionization and understanding the growth of supermassive black holes. Recent inferences of the luminosity function suffer from inconsistencies arising from inhomogeneous selection and analysis of AGN data. We address this problem by constructing a sample of more than 80,000 colour-selected AGN from redshift z=0 to 7.5. While this sample is composed of multiple data sets with spectroscopic redshifts and completeness estimates, we homogenise these data sets to identical cosmologies, intrinsic AGN spectra, and magnitude systems. Using this sample, we derive the AGN UV luminosity function from redshift z=0 to 7.5. The luminosity function has a double power law form at all redshifts. The break magnitude $M_*$ of the AGN luminosity function shows a steep brightening from $M_*sim -24$ at z=0.7 to $M_*sim -29$ at z=6. The faint-end slope $beta$ significantly steepens from $-1.7$ at $z<2.2$ to $-2.4$ at $zsimeq 6$. In spite of this steepening, the contribution of AGN to the hydrogen photoionization rate at $zsim 6$ is subdominant (< 3%), although it can be non-negligible (~10%) if these luminosity functions hold down to $M_{1450}=-18$. Under reasonable assumptions, AGN can reionize HeII by redshift z=2.9. At low redshifts (z<0.5), AGN can produce about half of the hydrogen photoionization rate inferred from the statistics of HI absorption lines in the IGM. Our global analysis of the luminosity function also reveals important systematic errors in the data, particularly at z=2.2--3.5, which need to be addressed and incorporated in the AGN selection function in future in order to improve our results. We make various fitting functions, luminosity function analysis codes, and homogenised AGN data publicly available.
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