The Astronomical Thermal Emission Camera (AzTEC) 1.1?mm survey of the two SCUBA HAlf Degree Extragalactic Survey (SHADES) fields is the largest (0.7?deg2) blank-field millimetre-wavelength (mm-wavelength) survey undertaken to date at a resolution of ?18?arcsec and a depth of ?1?mJy. We have used the deep optical to radio multiwavelength data in the SHADES Lockman Hole East and SXDF/UDS fields to obtain galaxy identifications for ?64 per cent (?80 per cent including tentative identifications) of the 148 AzTEC-SHADES 1.1?mm sources reported by Austermann et al., exploiting deep radio and 24 mu m data complemented by methods based on 8 mu m flux density and red opticalinfrared (i - K) colour. This unusually high identification rate can be attributed to the relatively bright mm-wavelength flux density threshold, combined with the relatively deep supporting multifrequency data now available in these two well-studied fields. We have further exploited the opticalmid-infraredradio data to derive an ?60 per cent (?75 per cent including tentative identifications) complete redshift distribution for the AzTEC-SHADES sources, yielding a median redshift of z ? 2.2, with a high-redshift tail extending to at least z ? 4. Despite the larger area probed by the AzTEC survey relative to the original SCUBA-SHADES imaging, the redshift distribution of the AzTEC sources is consistent with that displayed by the SCUBA sources, and reinforces tentative evidence that the redshift distribution of mm/submm sources in the Lockman Hole field is significantly different from that found in the SXDF/UDS field. Comparison with simulated surveys of similar scale extracted from semi-analytic models based on the Millennium simulation indicates that this is as expected if the mm/submm sources are massive (M > 1011?M?) star-forming galaxies tracing large-scale structures over scales of 1020?Mpc. This confirms the importance of surveys covering several deg2 (as now underway with SCUBA2) to obtain representative samples of bright (sub)mm-selected galaxies. This work provides a foundation for the further exploitation of the Spitzer and Herschel data in the SHADES fields in the study of the stellar masses and specific star formation rates of the most active star-forming galaxies in cosmic history.