We present the results of SCUBA observations of a complete sample of local ultraluminous infrared galaxies (ULIRGs). 20 of the initial sample of 23 sources are detected at 850 μm and nearly half of the objects are also detected at 450 μm. These data are combined with existing observations of a further seven ULIRGs to produce the largest sample of submillimetre observations of ULIRGs currently available. We use similar techniques to the SLUGS survey to fit dust spectral energy distributions (SEDs) to their far-IR emission. We find that ULIRGs have a higher dust temperature than lower luminosity objects (42 K compared to 35 K) and a steeper emissivity index. For those objects where 450 μm fluxes are available we also attempt a two component dust SED fit, with warm and cool dust and a dust emissivity index of β= 2. Such a model has been found to be a good fit to lower luminosity systems. We find that it also works well for ULIRGs, but that ULIRGs have a smaller cold dust component. Comparison of the dust mass derived for ULIRGs and more normal spiral galaxies suggests that the dust content of a ULIRG is simply the combined dust content of the two galaxies whose merger has triggered the ULIRG activity. We examine the high end of the 850 μm luminosity function and find results consistent with those of the earlier SLUGS survey. We also find that ULIRGs make up only about 50 per cent of the high end of the 850 μm luminosity function, with LIRGs containing a large mass of cool dust likely to be responsible for the rest.