Deep submillimetre (submm) observations using SCUBA are presented of the central regions of four high-redshift clusters which have been extensively studied optically: CL0023 + 0423 (z = 0 84), J0848 + 4453 (z = 1 27), CL1604 + 4304 (z = 0 90) and CL1604 + 4321 (z = 0 92). 10 submm sources are securely detected towards these four clusters at 850 mum, with two further tenuous detections; the raw 850-mum source counts exceed those determined from blank-field surveys by a factor similar to3-4. In particular, towards CL1604 + 4304, six sources are detected with S-850mum > 4 mJy making this the richest submm field discovered to date. Corrections for gravitational lensing by these high-redshift clusters reduce these excess sources counts, but are unlikely to account for more than about half of the excess, with the remainder presumably directly associated with cluster galaxies. The 450- to 850-mum flux density ratios of the detected sources are systematically higher (at a significance level > 98 per cent) than those determined for blank-field selected sources, consistent with them being at the cluster redshifts. If subsequent identifications confirm cluster membership, these results will demonstrate that the optical Butcher-Oemler effect is also observed at submm wavelengths.