We derive effective temperatures, luminosities and related parameters for a sample of eight Wolf-Rayet stars - seven WN stars and a WO star - by computing elaborate photoionization models of their surrounding ring nebulae. The most recent non-LTE WR model atmospheres are used for the input stellar ionizing flux distributions. The photoionization models have been constructed to match all possible observational data, such as shell diameters, radio fluxes and stellar optical continuum magnitudes. The fitting process uses planetary-nebula-type methods, and involves matching the main emission line ratios measured from ring nebulae observations reported in earlier papers in this series. All but one nebula (RCW 104) are modelled as hollow spheres surrounded by optically thin ionized shells. The derived effective temperatures T* range from 57000- 71000 K for the WN4-5 stars and <30 000-42 000 K for the WN6-8 stars with reasonable correlations between temperature and stellar radius R* and spectral subtype. The luminosities are broadly similar between WN subtypes and span a small range of 1.2-5.0 105 Lsun. We compare our derived stellar parameters with those obtained using other techniques, notably recent stellar emission line modelling. We find excellent agreement for the hot early WN stars, indicating that the non-LTE WR flux distributions are essentially correct, particularly in the crucial far-UV region. For the cooler late WN stars, we find lower temperatures and that the model flux distributions produce too much nebular ionization. We suggest that these discrepancies arise because of the lack of line-blanketing in the WR atmospheres. For the WO 1 central star of G 2.4+1.4, showing strong nebular He II 4686 Å emission, we derive a temperature of 105000 K, somewhat less than previous estimates. We compare the positions of our eight WR stars on the HR diagram with the evolutionary tracks of Maeder (1990) for solar metallicity. In common with previous workers, we find an initial mass range of 25-40 Msun, below that expected for the majority of WR stars. We also derive various nebular parameters including gas mass, ionization parameter U and optical depths. We find that the nebulae span a remarkably small range in U, from 0.7-2.6 1O-3, which is also typical of giant extragalactic H II regions. This uniformity in U appears to support the idea that stellar winds cause the ionizing flux and the shell gas density to scale closely with each other.