We present results of the first systematic search for submillimetre continuum emission from z=2, radio-quiet, optically-luminous quasars, using the SCUBA/JCMT. We have observed a homogeneous sample of 57 quasars in the redshift range 1.5<z<3.0- the epoch during which the comoving density of luminous AGN peaks- to make a systematic comparison with an equivalent sample at high (z>4) redshift. The target sensitivity of the survey (3sigma=10mJy at 850um) was chosen to enable efficient identification of bright submm sources, suitable for detailed follow-up. 9 targets are detected, with fluxes in the range 7-17mJy. Although there is a suggestion of variation of submm detectability between z=2 and z=4, this is consistent with the K-correction of a characteristic far-infrared spectrum. Additionally, the weighted mean fluxes of non-detections at z=2 and z>4 are comparable.