  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.
