We analyse 850um continuum observations of eight massive X-ray detected galaxy clusters at z~0.8-1.6 taken with SCUBA-2 on the James Clerk Maxwell Telescope. We find an average overdensity of 850um-selected sources of a factor of 4+/-2 per cluster within the central 1Mpc compared to the field. We investigate the multiwavelength properties of these sources and identify 34 infrared counterparts to 26 SCUBA-2 sources. Their colours suggest that the majority of these counterparts are probable cluster members. We use the multi-wavelength far-infrared photometry to measure the total luminosities and total cluster star-formation rates demonstrating that they are roughly three orders of magnitude higher than local clusters. We predict the H-band luminosities of the descendants of our cluster submillimetre galaxies and find that their stellar luminosity distribution is consistent with that of passive elliptical galaxies in z~0 clusters. Together, the faded descendants of the passive cluster population already in place at z~1 and the cluster submillimetre galaxies are able to account for the total luminosity function of early-type cluster galaxies at z~0. This suggests that the majority of the luminous passive population in z~0 clusters are likely to have formed at z>>1 through an extreme, dust-obscured starburst event.
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