We present a new catalogue of ∼2400 optically selected quasars with spectroscopic redshifts and X-ray observations from either Chandra or XMM–Newton. The sample can be used to investigate the non-linear relation between the ultraviolet (UV) and X-ray luminosity of quasars as well as to build a Hubble diagram up to a redshift of z ∼ 7.5. We selected sources that are neither reddened by dust in the optical and UV nor obscured by gas in the X-rays, and whose X-ray fluxes are free from flux-limit-related biases. After checking for any possible systematics, we confirm, in agreement with our previous works, that the X-ray to UV relation provides distance estimates matching those from supernovae up to z ∼ 1.5, and its slope shows no redshift evolution up to z ∼ 5. We provide a full description of the methodology for testing cosmological models, further supporting a trend whereby the Hubble diagram of quasars is well reproduced by the standard flat cold dark matter model up to z ∼ 1.5–2, but strong deviations emerge at higher redshifts. Since we have minimised all non-negligible systematic effects and proven the stability of the L_X − L_UV relation at high redshifts, we conclude that an evolution of the expansion rate of the Universe should be considered as a possible explanation for the observed deviation, rather than some systematic (redshift-dependent) effect associated with high-redshift quasars.