Radio and optical spectroscopy have been combined to measure chemical abundances in a large and representative sample of galactic H II regions covering a wide range in galactocentric radius RG. Radio recombination lines have been used to determine accurate electron temperatures in 67 H II regions spanning the range 3.5 < RG < 13.7 kpc and these temperatures have been applied to optical spectra of 33 of the same H II regions to determine the abundances of O, N, S, Ne and Ar in addition to He+. The derived electron temperatures are accurate to 5 per cent rms; uncertainties in the temperatures are dominated by observational factors – the non-LTE corrections are small (a few per cent) because of the careful matching of observing frequencies to the emission measures of the H II regions. There is good agreement between these electron temperatures and those obtained optically, and a tight correlation holds between Te and the optical line ratio ([O II] + [O III])/Hβ. Several exceptionally narrow recombination lines have been discovered, imposing absolute upper limits of 4000–5000 K on Te from the linewidths alone and establishing beyond any doubt the existence of low-temperature H II regions. A temperature gradient of 433 ± 40 K kpc−1 is found. It is consistent with the derived metallicity gradient, on the assumption that the temperature gradient is purely an abundance effect. At any given galactocentric distance there is a spread in Te of ∼ 2000 K, which is due largely to differences in electron densities and the effective temperatures of the exciting stars. The oxygen abundance gradient is −0.07 ± 0.015 dex kpc−1. That of nitrogen is not much steeper, −0.09 ± 0.015 dex kpc−1. Sulphur appears to have a significantly flatter abundance gradient, −0.01 ± 0.02 dex kpc−1. Neon may also have a relatively flat abundance gradient, but that for argon is very similar to the oxygen abundance gradient. These gradients may be somewhat steeper in the inner regions of the galactic disc. Local abundance variations (at a given galactocentric distance) are small, less than 20 per cent rms. No significant gradient has been found in the He+/H+ ratio.