This paper is the second in a series of two on the UV continuum emission (in the range from 1400 to 3700 A) of radio galaxies that were extracted from the Hubble Space Telescope (HST) Archives. The sample consists of 31 3C and Parkes radio galaxies that have redshifts below 0.2 (the majority have redshifts of ~0.03) and radio powers of ~1025–1027 W Hz-1 (using H0 = 50 km-1 s-1 Mpc and q0 = 0.0). Paper I describes the sample selection and the properties of individual sources; this paper deals with the analysis. We find that only about half the radio galaxies display any UV flux at wavelengths shorter than 2300 A. More specifically, those galaxies that are dominated by a nuclear UV component are either BL Lac objects or radio galaxies with broad emission lines. We detect a nuclear and an extended UV component only among half the radio galaxies with narrow emission lines. Although we do not find a correlation of the UV luminosity with emission-line luminosity or radio power, there does appear to be a dependence on radio morphology. While (narrow line) FR II sources do not show a nuclear UV component, FR I's do, however, only if they also have an optical jet (this is the case for seven of 21 FR I's). These results are broadly consistent with orientation-dependent unification models. In radio galaxies in which the torus does not obscure our view of the engine, the observed UV radiation appears to be point source–like. This is the case for broad-line radio galaxies and BL Lac objects. In other radio galaxies that are oriented at an angle to us, the torus presumably blocks the nuclear UV component. The narrow-line FR I galaxies with optical jets can then be interpreted as objects at a critical angle at which some, but not all, nuclear UV emission is blocked. The UVλ luminosities (with λ ranging from 1400 to 3700 A) and the UVλ-V colors of radio galaxies show a larger scatter than those of radio-quiet elliptical galaxies. At wavelengths shorter than 2300 A, some radio galaxies have on average bluer colors, but beyond 3000 A, their colors are on average slightly redder. This picture is also consistent with unification models—the galaxies with bluer colors are either BL Lac objects or broad-line radio galaxies. All other radio galaxies (including the jetted FR I's) have somewhat redder colors than radio-quiet elliptical galaxies. We suspect that this is primarily due to reddening by dust, which we know is present in some of the radio galaxies in the sample. At longer wavelengths (>3000 A), all radio galaxies (14 of 14) show an extended component. The morphology of the extended emission is in most, but not all, cases comparable to the morphology at optical wavelengths, implying that this is likely to be starlight. However, the polarization images of two of seven radio galaxies indicate that scattered light from the active galactic nucleus may also contribute toward the UV luminosity.