The AzTEC 1.1 mm survey of the SCUBA HAlf Degree Extragalactic Survey (SHADES) fields is the largest (0.7 deg2) blank-field millimetre-wavelength survey undertaken to date at a resolution of ~18" and a depth of ~1 mJy. We have used the deep optical-to-radio multi-wavelength data in the SHADES Lockman Hole East and SXDF/UDS fields to obtain galaxy identifications for ~64% (~80% with tentative identifications) of the 148 AzTEC-SHADES 1.1 mm sources, exploiting deep radio and 24 um data complemented by methods based on 8 um flux-density and red optical-infrared (i-K) colour. This unusually high identification rate can be attributed to the relatively bright millimetre-wavelength flux-density threshold, combined with the relatively deep supporting multi-frequency data. We have further exploited the optical-mid-infrared-radio data to derive a ~60% (~75% with 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/sub-mm 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/sub-mm sources are massive (M>10^11 Mo) star-forming galaxies tracing large-scale structures over scales of 10-20 Mpc. This confirms the importance of surveys covering several square degrees (as now underway with SCUBA2) to obtain representative samples of bright (sub)mm-selected galaxies.