Spatially resolved long-slit spectrophotometric data for the planetary nebulae PB 6, NGC 2452, NGC 2867, NGC 6905 and He 2-55 are presented. Different knots were observed in each nebula. All the nebulae are ionized by [WC 2-3] type nuclei. For the five objects, we calculated photoionization models using the ionizing radiation field from models of expanding atmospheres. The photoionization models, built with the condition that the predicted stellar visual magnitude is equal to the observed one, were rather successful in reproducing at the same time the ionization structure and the electron temperature of the nebulae, using model atmospheres that were close (+/-20 000 K) to the best fit for reproducing the stellar features, as presented by Koesterke & Hamann (1997a). The constraints for the modelling procedure were to reproduce the observed intensity ratios of important lines of different ionization stages, and to be roughly consistent with the observed Hβ flux, angular diameter and morphology of the nebulae. We found that, for some objects, only two-density models with an inner zone of lower density can meet all these requirements. These density structures are consistent with the morphology showed by the nebulae. In a couple of cases, our photoionization modelling seems to indicate that the models of expanding atmospheres used could be lacking ionizing photons with respect to their emission in the V band. Chemical abundances in the nebulae were derived from the ionic abundances observed and ionization correction factors obtained from the models. We found that, while the five nebulae of our program have very similar exciting stars (similar stellar temperatures, mass loss rates, chemical compositions), the nebular chemical compositions are different. PB 6 and NGC 2452 are He-, N-, and probably C-rich nebulae, indicating massive progenitors (M_initial >= 2.8 M_sun). In particular, abundances in PB 6 are consistent with a scenario of C produced via the triple-alpha process, being brought to the surface by the third dredge-up event and partially converted into N through envelope-burning. The other nebulae present typical disk-PNe abundances, showing only C enrichment (C/O >= 1). Therefore their progenitors were not massive, but all underwent the third dredge-up. Thus, clearly, post-AGB stars of quite different initial masses can pass through a [WC] stage with similar atmospheric parameters. We did not find evidence for abundance variations inside any of the nebulae. In PB 6 and NGC 2867, we found that the C/O ratios derived from the C Iii] 1909/[O Iii] 5007 line ratios would induce electron temperatures significantly lower than observed. The discrepancy would be larger if carbon abundances derived from the optical C Ii 4267 recombination lines are considered. Partially based on data obtained at the Observatorio Astronómico Nacional, SPM, B.C., México