  The design, optimisation and construction of an anti-coincidence veto
detector to complement the ZEPLIN-III direct dark matter search instrument is
described. One tonne of plastic scintillator is arranged into 52 bars
individually read out by photomultipliers and coupled to a gadolinium-loaded
passive polypropylene shield. Particular attention has been paid to
radiological content. The overall aim has been to achieve a veto detector of
low threshold and high efficiency without the creation of additional background
in ZEPLIN-III, all at a reasonable cost. Extensive experimental measurements of
the components have been made, including radioactivity levels and performance
characteristics. These have been used to inform a complete end-to-end Monte
Carlo simulation that has then been used to calculate the expected performance
of the new instrument, both operating alone and as an anti-coincidence detector
for ZEPLIN-III. The veto device will be capable of rejecting over 65% of
coincident nuclear recoil events from neutron background in the energy range of
interest in ZEPLIN-III. This will reduce the background in ZEPLIN-III from ~0.4
to ~0.14 events per year in the WIMP acceptance region, a significant factor in
the event of a non-zero observation. Furthermore, in addition to providing
valuable diagnostic capabilities, the veto is capable of tagging over 15% for
gamma-ray rejection, all whilst contributing no significant additional
background. In conjunction with the replacement of the internal ZEPLIN-III
photomultiplier array, the new veto is expected to improve significantly the
sensitivity of the ZEPLIN-III instrument to dark matter, allowing spin
independent WIMP-nucleon cross sections below 1E-8 pb to be probed.
