We have obtained spectroscopic observations of the nebulae around seven Wolf–Rayet (WR) stars, four in the Milky Way (WR 8, 16, 18 and 40) and three in the Large Magellanic Cloud (LMC; BAT99-2, -11 and -38). They were observed using the European Southern Observatory (ESO) New Technology Telescope (NTT) with the EFOSC-2 instrument, except for one nebula, NGC 3199, which was observed using the UVES echelle spectrometer on the Very Large Telescope (VLT). The aims of these observations were to (a) quantify the degree of chemical enrichment in WR nebulae which had previously been suggested to have abundances reflecting nucleosynthetic processing; and (b) to attempt to detect the far-red lines of neutral carbon (e.g. [C i] 9850 Å) in the nebulae around carbon-rich WR (WC) stars. Nebular densities, temperatures and elemental abundances were derived using standard emission line diagnostics. For those nebulae for which the usual temperature diagnostic lines were not detected, their measured [N ii] and [O ii] line intensities were used to derive reliable N/O ratios. Our high spectral resolution UVES data set for NGC 3199 allowed the determination of line broadening temperatures using lines from several different species. These showed consistent patterns and fair agreement with the nebular temperatures derived from diagnostic line ratios. Amongst the Galactic WR nebulae, the nebulae around WR 8, 16 and 40 were found to be strongly nitrogen-enriched. NGC 3199 displayed abundances which were very similar to those of Galactic H ii regions, in agreement with previous analyses and consistent with the inference that it is a shell of swept-up interstellar gas. Amongst the LMC WR nebulae, none displayed an N/O ratio that significantly exceeded LMC H ii region values. The far-red [C i] lines were detected from NGC 3199, with the strength of the 8727 Å line indicating that at least part of it was produced by C+ recombination rather than collisional excitation. The linewidths of the [C i] 9824 and 9850 Å lines were, however, the same as those of collisionally excited nebular lines, indicating that those lines originated largely from ionized regions within the nebula.