  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 galaxy's properties in a brief period of cosmic time.
