We present submillimetre and mid-infrared imaging observations of five fields centred on quasi-stellar objects (QSOs) at 1.7<z<2.8. All 5 QSOs were detected previously at submillimetre wavelengths. At 850 (450) um we detect 17 (11) submillimetre galaxies (SMGs) in addition to the QSOs. The total area mapped at 850 um is ~28 arcmin^2 down to RMS noise levels of 1-2 mJy/beam, depending on the field. Integral number counts are computed from the 850 um data using the same analytical techniques adopted by `blank-field submillimetre surveys. We find that the `QSO-field counts show a clear excess over the blank-field counts at deboosted flux densities of 2-4 mJy; at higher flux densities the counts are consistent with the blank-field counts. Robust mid-infrared counterparts are identified for all four submillimetre detected QSOs and ~60 per cent of the SMGs. The mid-infrared colours of the QSOs are similar to those of the local ULIRG/AGN Mrk 231 if placed at 1<z<3 whilst most of the SMGs have colours very similar to those of the local ULIRG Arp 220 at 1<z<3. Mid-infrared diagnostics therefore find no strong evidence that the SMGs host buried AGN although we cannot rule out such a possibility. Taken together our results suggest that the QSOs sit in regions of the early universe which are undergoing an enhanced level of major star-formation activity, and should evolve to become similarly dense regions containing massive galaxies at the present epoch. Finally, we find evidence that the level of star-formation activity in individual galaxies appears to be lower around the QSOs than it is around more powerful radio-loud AGN at higher redshifts.
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