We investigate the properties of the galaxies selected from the deepest 850-{mu}m survey undertaken to date with (Submillimetre Common-User Bolometer Array 2) SCUBA-2 on the James Clerk Maxwell Telescope as part of the SCUBA-2 Cosmology Legacy Survey. A total of 106 sources (>5{sigma}) were uncovered at 850{mu}m from an area of ~=150 arcmin^2^ in the centre of the COSMOS/UltraVISTA/Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) field, imaged to a typical depth of {sigma}_850_~=0.25mJy. We utilize the available multifrequency data to identify galaxy counterparts for 80 of these sources (75 per cent), and to establish the complete redshift distribution for this sample, yielding . We have also been able to determine the stellar masses of the majority of the galaxy identifications, enabling us to explore their location on the star formation rate:stellar mass (SFR:M*) plane. Crucially, our new deep 850-{mu}m-selected sample reaches flux densities equivalent to SFR~=100M_{sun}_/yr, enabling us to confirm that sub-mm galaxies form the high-mass end of the 'main sequence' (MS) of star-forming galaxies at z>1.5 (with a mean specific SFR of sSFR=2.25+/-0.19Gyr^-1^ at z~=2.5). Our results are consistent with no significant flattening of the MS towards high masses at these redshifts. However, our results add to the growing evidence that average sSFR rises only slowly at high redshift, resulting in log_10_sSFR being an apparently simple linear function of the age of the Universe.