At low redshift, early-type galaxies often exhibit a rising flux with decreasing wavelength in the 1000-2500{AA} range, called "UV upturn". The origin of this phenomenon is debated, and its evolution with redshift is poorly constrained. The observed GALEX FUV-NUV color can be used to probe the UV upturn up to redshift about 0.5. We aim to provide constraints on the existence of the UV upturn up to redshift ~0.4 in Brightest Cluster Galaxies (BCG) galaxies located behind the Virgo cluster, using data from the GUViCS survey. We estimate the FUV and NUV observed magnitudes for BCGs from the maxBCG catalog in the GUViCS fields. We increase the number of non local galaxies identified as BCGs with GALEX photometry from a few tens of galaxies to 166 (64 when restricting this sample to relatively small error-bars). We also estimate a central color within a 20-arcsec aperture. By using the r band luminosity from the maxBCG catalog, we can separate blue FUV-NUV due to recent star formation and candidate upturn cases. We use Lick indices to verify their similitude to redshift 0 upturn cases. We clearly detect a population of blue FUV-NUV BCGs in the redshift range 0.10-0.35, vastly improving the existing constraints at these epochs by increasing the number of galaxies studied, and by exploring a redshift range with no previous data (beyond 0.2), spanning 1 more Gyr in the past. These galaxies bring new constrains that can help distinguish between assumptions concerning the stellar populations causing the UV upturn phenomenon. The existence of a large number of UV upturns around redshift 0.25 favors the existence of a binary channel among the sources proposed in the literature.