Context. The study of the radial variations of metallicity across the Galactic disc is a powerful method for understanding the history of star formation and chemical evolution of the Milky Way. Although several studies about gradients have been performed so far, the knowledge of the Galactic antincentre is still poor. Aims: This work aims to determine accurately the physical and chemical properties of a sample of H ii regions located at RG > 11 kpc and to study the radial distribution of abundances in the outermost part of the Galaxy disc. Methods: We carried out new optical spectroscopic observations of nine H ii regions with the William Herschel Telescope covering the spectral range from 3500 Å to 10 100 Å. In addition, we increased the sample by searching the literature for optical observations of regions towards the Galactic anticentre, re-analysing them to obtain a single sample of 23 objects to be processed in a homogeneous and consistent manner. The total sample distribution covers the Galactocentric radius from 11 kpc to 18 kpc. Results: Emission line ratios were used to determine accurate electron densities and temperatures of several ionic species in 13 H ii regions. These physical parameters were applied to the spectra to determine direct total chemical abundances. For those regions without direct estimations of temperature, chemical abundances were derived by performing tailor-made photoionisation models and/or by using an empirical relation obtained from radio recombination and optical temperatures. We performed weighted least-squares fits to the distribution of the derived abundances along the Galactocentric distances to study the radial gradients of metallicity across the outermost part of the MW. The distributions O/H, N/H, S/H, and Ar/H towards the anticentre can be represented by decreasing linear radial gradients, while in the case of N/O abundances the radial distribution is better fitted with a two-zone model. The He/H radial gradient is presented here for the first time; we find a slope that is not significantly different from zero. The derived gradient for oxygen shows a clear decrease with distance with a slope of -0.053 ± 0.009 dex kpc-1. Although a shallower slope at large Galactocentric distances is suggested by our data, the flattening of the distribution cannot be confirmed and more objects towards the anticentre need to be studied in order to establish the true form of the metallicity gradient.