We have studied the nuclei of 28 radio galaxies from the 3CR sample in the UV band. Unresolved nuclei (central compact cores: CCCs) are observed in 10 of the 13 FR I galaxies, and in five of the 15 FR II galaxies. All sources that do not have a CCC in the optical do not have a CCC in the UV. Two FR I galaxies (3C 270 and 3C 296) have a CCC in the optical but do not show the UV counterpart. Both of them show large dusty disks observed almost edge-on, possibly implying that they play a role in obscuring the nuclear emission. We have measured optical-UV spectral indices o,UV between $0.6 and $7.0 (F / À ). Broad-line radio galaxies have the flattest spectra, and their values of o,UV are also confined to a very narrow range. This is consistent with radiation produced in a geometrically thin, optically thick accretion disk. On the other hand, FR I nuclei, which are most plausibly originated by synchrotron emission from the inner relativistic jet, show a wide range of o,UV . There is a clear trend with orientation in that sources observed almost edge-on or with clear signs of dust absorption have the steepest spectra. These observations imply that in FR I galaxies, obscuration can be present, but the obscuring material is not in a '' standard '' geometrically thick torus. The most striking difference between these absorbing structures and the classic active galactic nucleus '' tori '' resides in the lower optical depth of the FR I galaxy obscuring material.