The so-called ultraviolet (UV) upturn of elliptical galaxies is a phenomenon characterised by the up-rise of their fluxes in bluer wavelengths, typically in the 1,200-2,500 A range. This work aims at estimating the rate of occurrence of the UV upturn over the entire red-sequence population of galaxies that show significant UV emission. This assessment is made considering it as function of three parameters: redshift, stellar mass, and -what may seem counter-intuitive at first -emission-line classification. We built a multiwavelength spectro-photometric catalogue from the Galaxy Mass Assembly survey, together with aperture-matched data from Galaxy Evolution Explorer and Sloan Digital Sky Survey, covering the redshift range between 0.06 and 0.40. From this sample, we analyse the UV emission among UV bright galaxies, by selecting those that occupy the red-sequence locus in the (NUV-r) × (FUV-NUV) chart; then, we stratify the sample by their emission-line classes. To that end, we make use of emission-line diagnostic diagrams, focusing the analysis in retired/passive lineless galaxies. Then, a Bayesian logistic model was built to simultaneously deal with the effects of all galaxy properties (including emission-line classification or lack thereof). The main results show that retired/passive systems host an up-rise in the fraction of UV upturn for redshifts between 0.06 and 0.25, followed by an in-fall up to 0.35. Additionally, we show that the fraction of UV upturn hosts rises with increasing stellar mass.