We present deep optical spectroscopy of eight H II regions located in the anti-centre of the Milky Way. The spectra were obtained at the 10.4 m GTC and 8.2 m VLT. We determined Te([N II]) for all objects and Te([O III]) for six of them. We also included in our analysis an additional sample of 13 inner-disc Galactic H II regions from the literature that have excellent Te determinations. We adopted the same methodology and atomic data set to determine the physical conditions and ionic abundances for both samples. We also detected the C II and O II optical recombination lines in Sh 2-100, which enables the determination of the abundance discrepancy factor for this object. We found that the slopes of the radial oxygen gradients defined by the H II regions from R25 (=11.5 kpc) to 17 kpc and those within R25 are similar within the uncertainties, indicating the absence of flattening in the radial oxygen gradient in the outer Milky Way. In general, we found that the scatter of the O/H ratios of H II regions is not substantially larger than the observational uncertainties. The largest possible local inhomogeneities of the oxygen abundances are of the order of 0.1 dex. We also found positive radial gradients in Te([O III]) and Te([N II]) across the Galactic disc. The shapes of these temperature gradients are similar and also consistent with the absence of flattening of the metallicity distribution in the outer Galactic disc.