Herbig Ae/Be stars (HAeBes) span a key mass range that links low- and high-mass stars, and thus provide an ideal window from which to explore their formation. This paper presents Very Large Telescope/X-shooter spectra of 91 HAeBes, the largest spectroscopic study of HAeBe accretion to date. A homogeneous approach to determining stellar parameters is undertaken for the majority of the sample. Measurements of the ultraviolet are modelled within the context of magnetospheric accretion, allowing a direct determination of mass accretion rates. Multiple correlations are observed across the sample between accretion and stellar properties: the youngest and often most massive stars are the strongest accretors, and there is an almost 1:1 relationship between the accretion luminosity and stellar luminosity. Despite these overall trends of increased accretion rates in HAeBes when compared to classical T Tauri stars, we also find noticeable differences in correlations when considering the Herbig Ae and Herbig Be subsets. This, combined with the difficulty in applying a magnetospheric accretion model to some of the Herbig Be stars, could suggest that another form of accretion may be occurring within Herbig Be mass range.