The object 4C 71.07 is a high-redshift blazar whose spectral energy distribution shows a prominent big blue bump and a strong Compton dominance. We present the results of a 2-yr multiwavelength campaign led by the Whole Earth Blazar Telescope (WEBT) to study both the quasar core and the beamed jet of this source. The WEBT data are complemented by ultraviolet and X-ray data from Swift, and by γ-ray data by Fermi. The big blue bump is modelled by using optical and near-infrared mean spectra obtained during the campaign, together with optical and ultraviolet quasar templates. We give prescriptions to correct the source photometry in the various bands for the thermal contribution, in order to derive the non-thermal jet flux. The role of the intergalactic medium absorption is analysed in both the ultraviolet and X-ray bands. We provide opacity values to deabsorb ultraviolet data, and derive a best-guess value for the hydrogen column density of N_H^best=6.3 × 10^{20} cm^{-2} through the analysis of X-ray spectra. We estimate the disc and jet bolometric luminosities, accretion rate, and black hole mass. Light curves do not show persistent correlations among flux changes at different frequencies. We study the polarimetric behaviour and find no correlation between polarization degree and flux, even when correcting for the dilution effect of the big blue bump. Similarly, wide rotations of the electric vector polarization angle do not seem to be connected with the source activity.