Work contributing to experimental limits on WIMP dark matter scattering in a liquid xenon target is presented. The ZEPLIN-III detector at Boulby completed 83 days’ continuous operation in 2008 and, following a hardware upgrade, a further 319 days in 2010–11. Inelastic dark matter hypotheses to explain the DAMA/LIBRA modulation as scattering from iodine are excluded with ≥ 87% confidence using 2008 data. Upper limits on the elastic WIMP-nucleon cross section are set from the combined exposure, with a minimum of 3.9 × 10⁻⁸ pb for 50 GeVc⁻² WIMP mass at 90% CL, in addition to competitive limits on the WIMP-neutron spin-dependent cross section. The detector responses to scintillation and ionisation—throughout the fiducial volume and over the duration of the run — are characterised via calibration with ⁵⁷Co and ¹³⁷Cs sources, as well as sidebands in search data. Signal spectra are modeled using these responses and an in situ measurement of the energy-dependent light and charge yields of nuclear recoils. Analysis software, event selection and background estimation are all described. Confidence intervals based on sparse regions of parameter space (Yellin limits) and the likelihood ratios are implemented for ZEPLIN-III and discussed in the context of rare-event searches with significant background uncertainty.