We present the first study of the far-infrared (FIR) properties of high-redshift, radio-selected ultraluminous infrared galaxies (ULIRGs) using deep observations obtained with the Spectral and Photometric Imaging Receiver (SPIRE) from the Herschel Multi-tiered Extragalactic Survey (HerMES). These galaxies span a large range of 850-um fluxes from submillimetre-luminous ~10mJy sources (SCUBA galaxies) to ~1.5mJy from stacked SCUBA non-detections, thus likely representing a complete distribution of ULIRG spectral energy distributions (SEDs). From Keck spectroscopic surveys in the Lockman-North field we identified a sample of 31 submillimetre galaxies (SMGs) and 37 submillimetre-faint, optically faint radio galaxies (OFRGs), all with radio-inferred IR luminosities >10^12^L_{sun}_. These galaxies were cross-identified with SPIRE 250-, 350- and 500-um catalogues based on fluxes extracted at 24-um positions in the SWIRE survey, yielding a sample of more than half of the galaxies well detected in at least two of the SPIRE bandpasses.