We present the optical-to-submillimetre spectral energy distributions (SEDs) for 33 radio and mid-infrared (mid-IR) identified submillimetre galaxies discovered via the SHADES 850-μm SCUBA imaging in the Subaru-XMM Deep Field (SXDF). Optical data for the sources come from the SXDF and mid- and far-IR fluxes from SWIRE. We obtain photometric redshift estimates for our sources using optical and IRAC 3.6- and 4.5-μm fluxes. We then fit SED templates to the longer wavelength data to determine the nature of the far-IR emission that dominates the bolometric luminosity of these sources. The IR template fits are also used to resolve ambiguous identifications and cases of redshift aliasing. The redshift distribution obtained broadly matches previous results for submillimetre sources and on the SHADES SXDF field. Our template fitting finds that active galactic nuclei, while present in about 10 per cent of our sources, do not contribute significantly to their bolometric luminosity. Dust heating by starbursts, with either Arp220 or M82 type SEDs, appears to be responsible for the luminosity in most sources (23/33 are fitted by Arp220 templates, 2/33 by the warmer M82 templates). 8/33 sources, in contrast, are fitted by a cooler cirrus dust template, suggesting that cold dust has a role in some of these highly luminous objects. Three of our sources appear to have multiple identifications or components at the same redshift, but we find no statistical evidence that close associations are common among our SHADES sources. Examination of rest-frame K-band luminosity suggests that `downsizing' is underway in the submillimetre galaxy population, with lower redshift systems lying in lower mass host galaxies. Of our 33 identifications six are found to be of lower reliability but their exclusion would not significantly alter our conclusions.