We present the redshift distribution of the SHADES galaxy population based on the rest-frame radio-mm-FIR colours of 120 robustly detected 850μm sources in the Lockman Hole East (LH) and Subaru XMM-Newton Deep Field (SXDF). The redshift distribution derived from the full SED information is shown to be narrower than that determined from the radio–submm spectral index, as more photometric bands contribute to a higher redshift accuracy. The redshift distribution of sources derived from at least two photometric bands peaks at z ≈ 2.4 and has a near-Gaussian distribution, with 50 per cent (interquartile range) of sources at z = 1.8 − 3.1. We find a statistically-significant difference between the measured redshift distributions in the two fields; the SXDF peaking at a slightly lower redshift (median z≈ 2.2) than the LH (median z≈ 2.7), which we attribute to the noise-properties of the radio observations. We demonstrate however that there could also be field-to-field variations that are consistent with the measured differences in the redshift distributions, and hence, that the incomplete area observed by SHADES with SCUBA, despite being the largest sub-mm survey to date, may still be too small to fully characterize the bright sub-mm galaxy population. Finally we present a brief comparison with the predicted, or assumed, redshift distributions of sub-mm galaxy formation and evolution models, and we derive the contribution of these SHADES sources and the general sub-mm galaxy population to the star formation-rate density at different epochs.