The 3CRR sample of radio galaxies and quasars has been cross-correlated with the ROSAT PSPC All-Sky Survey. About 25 per cent of the objects have been detected in the 0.2-2.4 keV range, the large majority being powerful radio and X-ray emitters with a range of X-ray luminosities between 10(44) and 10(46) erg s(-1). The 0.2-2.4 keV spectrum of the radio-loud sources is found to be well characterized by a single power-law continuum absorbed by typical Galactic H column densities. The range of power-law spectral indices ( -1.5 < alpha < -0.2) clusters around alpha similar to - 1, and is in general steeper than those measured for radio-loud sources at energies above 2 keV. Thus, the presence of a soft X-ray excess component in radio-loud sources is found to be a common feature in the spectrum of these objects. This soft excess appears to be of the same nature as that seen in their radio-quiet counterparts, the only difference being a slight steepening of the spectrum in the latter. Emphasis is put on the close similarity between the radio and the high-energy (typically 2-10 keV) spectral indices for the lobe-dominated sources in the sample. Although in only five of the sources could an individual cross-checking be performed, there is an overall agreement between the radio and the hard X-ray spectral slopes in lobe-dominated sources, which is suggestive of a similar spectral distribution of particle energy in the core and in the lobes of radio sources.