Although attempts have been made to constrain the stellar types of optical counterparts to ULXs, the detection of optical variability instead suggests that they may be dominated by reprocessed emission from X-rays which irradiate the outer accretion disc. Here, we report results from a combined X-ray and optical spectral study of a sample of ULXs, which were selected for having broadened disc-like X-ray spectra, and known optical counterparts. We simultaneously fit optical and X-ray data from ULXs with a new spectral model of emission from an irradiated, colour-temperature-corrected accretion disc around a black hole, with a central Comptonising corona. We find that the ULXs require reprocessing fractions of $∼ 10^{-3}$, which is similar to sub-Eddington thermal dominant state BHBs, but less than has been reported for ULXs with soft ultraluminous X-ray spectra. We suggest that the reprocessing fraction may be due to the opposing effects of self-shielding in a geometrically thick super-critical accretion disc, and reflection from far above the central black hole by optically thin material ejected in a natal super-Eddington wind. Then, the higher reprocessing fractions reported for ULXs with wind-dominated X-ray spectra may be due to enhanced scattering onto the outer disc via the stronger wind in these objects. Alternatively, the accretion discs in these ULXs may not be particularly geometrically thick, rather they may be similar in this regard to the thermal dominant state BHBs. ; Comment: Accepted for publication in MNRAS; 16 pages, 4 figures, 5 tables