The old, red stars which constitute the bulges of galaxies, and the massive black holes at their centres, are the relics of a period in cosmic history when galaxies formed stars at remarkable rates and active galactic nuclei (AGN) shone brightly from accretion onto black holes. It is widely suspected, but unproven, that the tight correlation in mass of the black hole and stellar components results from the AGN quenching the surrounding star formation as it approaches its peak luminosity. X-rays trace emission from AGN unambiguously, while powerful star-forming galaxies are usually dust-obscured and are brightest at infrared to submillimetre wavelengths. Here we report observations in the submillimetre and X-ray which show that rapid star formation was common in the host galaxies of AGN when the Universe was 2-6 Gyrs old, but that the most vigorous star formation is not observed around black holes above an X-ray luminosity of 10^44 erg/s. This suppression of star formation in the host galaxies of powerful AGN is a key prediction of models in which the AGN drives a powerful outflow, expelling the interstellar medium of its host galaxy and transforming the galaxys properties in a brief period of cosmic time.
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