We investigate whether the far-UV continuum of nearby radio galaxies is due solely to the parent galaxy that passively evolves, or if it reveals evidence for the presence of other star-forming or non-stellar components. If the UV excess is due to an additional radiation component, we compare this with other properties such as radio power, optical spectral type (e.g. high- and low-excitation galaxies), and the strength of the emission lines. We also discuss the possible correlation between the ultraviolet flux, IR properties, and the central black hole mass. We used a sample of low-luminosity B2 radio galaxies and a small sample of higher luminosity 3C radio galaxies at comparable redshift (z<0.2). Spectral energy distributions (SEDs) were constructed using a number of on-line databases that are freely available now: GALEX, SDSS, 2MASS, and WISE. These were compared with model SEDs of early-type galaxies with passively evolving stellar populations at various ages (typically 0.5-1.3x10^9^ years). We established whether a second component was needed to obtain a satisfactory fit with the observed overall SED. We introduce the parameter XUV, which measures the excess slope of the UV continuum between 4500 and 2000{AA} with respect to the UV radiation produced by the underlying old galaxy component. We find that the UV excess as measured by XUV is usually small or absent in low-luminosity (FR I) sources, but sets in abruptly at the transition radio power, above which we find mostly FRII sources. XUV behaves very similarly to the strength of the optical emission lines (in particular H{alpha}). Below P_1.4GHz_<10^24^W/Hz XUV is close to zero. XUV correlates strongly with the H{alpha} line strength, but only in sources with strong H{alpha} emission. We discuss whether the line emission might be due to photoionization by radiation from the parent galaxy, possibly with additional star formation, or if it requires the presence of a non-stellar active galactic nucleus component. XUV and the slope of the mid-IR are strongly correlated, as measured by the WISE bands in the interval 3.4 to 22{mu}m, in the sense that sources with a strong UV excess also have stronger IR emission. There is an inverse correlation between XUV and central black hole mass: the M_BH_ of objects with strong UV excess is on average two to three times less massive than that of objects without UV excess. Low-luminosity radio galaxies tend to be more massive and contain more massive black holes.