We exploit stellar population models of absorption line indices in the ultraviolet (from 2000 to 3200 Å) to study the spectra of massive galaxies. Our central aim is to investigate the occurrence at high redshift of the UV upturn, i.e. the increased UV emission due to old stars observed in massive galaxies and spiral bulges in the local Universe. We use a large (∼275 000) sample of z ∼ 0.6 massive (M*/M⊙ > 11.5) galaxies using both individual spectra and stacks and employ a suite of models including a UV contribution from old populations, spanning various effective temperatures, fuel consumptions and metallicities. We find that a subset of our indices; Mg I, Fe I, and BL3096, are able to differentiate between old and young UV ages. We find evidence for old stars contributing to the UV in massive galaxies, rather than star formation. The data favour models with low/medium upturn temperatures (10 000–25 000 K) consistent with local galaxies, depending on the assumed metallicity, and with a larger fuel (f∼6.5×10−2M⊙f∼6.5×10−2M⊙). Models with one typical temperature are favoured over models with a temperature range, which would be typical of an extended horizontal branch. Old UV-bright populations are found in the whole galaxy sample (92 per cent), with a mass fraction peaking around 20–30 per cent. Upturn galaxies are massive and have redder colours, in agreement with findings in the local Universe. We find that the upturn phenomenon appears at z ∼ 1 and its frequency increases towards lower redshift, as expected by stellar evolution of low-mass stars. Our findings will help constrain stellar evolution in the exotic UV upturn phase.