Herbig Ae/Be stars lie in the mass range between low and high mass young stars, and therefore offer a unique opportunity to observe any changes in the formation processes that may occur across this boundary. This paper presents medium resolution VLT/X-Shooter spectra of six Herbig Ae/Be stars, drawn from a sample of 91 targets, and high resolution VLT/CRIRES spectra of five Herbig Ae/Be stars, chosen based on the presence of CO first overtone bandhead emission in their spectra. The X-Shooter survey reveals a low detection rate of CO first overtone emission (7 per cent), consisting of objects mainly of spectral type B. A positive correlation is found between the strength of the CO v=2-0 and Br {gamma} emission lines, despite their intrinsic linewidths suggesting a separate kinematic origin. The high resolution CRIRES spectra are modelled, and are well fitted under the assumption that the emission originates from small scale Keplerian discs, interior to the dust sublimation radius, but outside the co-rotation radius of the central stars. In addition, our findings are in very good agreement for the one object where spatially resolved near-infrared interferometric studies have also been performed. These results suggest that the Herbig Ae/Be stars in question are in the process of gaining mass via disc accretion, and that modelling of high spectral resolution spectra is able to provide a reliable probe into the process of stellar accretion in young stars of intermediate to high masses.