This paper is part of a series devoted to the investigation of a large sample of brightest cluster galaxies (BCGs), their properties and the relationships between these properties and the properties of the host clusters. In this paper, we compare the stellar population properties derived from high signal-to-noise ratio, optical long-slit spectra with the Galaxy Evolution Explorer (GALEX) ultraviolet (UV) colour measurements for 36 nearby BCGs to understand the diversity in the most rapidly evolving feature in old stellar systems, the UV upturn. We investigate (1) the possible differences between the UV upturn of BCGs and that of a control sample of ordinary ellipticals in the same mass range, as well as possible correlations between the UV upturn and other general properties of the galaxies; (2) the possible correlations between the UV upturn and the properties of the host clusters and (3) the recently proposed scenarios where helium sedimentation in the cluster centre can produce an enhanced UV upturn. We find systematic differences between the UV colours of BCGs and ordinary ellipticals, but we do not find correlations between these colours and the properties of the host clusters. Furthermore, the observations do not support the predictions made by the helium-sedimentation model as an enhancer of the UV upturn. ; http://dx.doi.org/10.1111/j.1365-2966.2010.17666.x ; http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2010.17666.x/pdf