An analysis of CCD spectra in the range lambda lambda4200 -8775, obtained at several positions of seven bright Galactic H Ii regions, with galactocentric distances in the range 6-10 kpc, is presented. Temperatures, densities and ionic abundances are calculated for all the positions, and the relative trends followed by these parameters are established. It is shown that all these H Ii regions share the same abundances of element{O}, element{S}, element{Cl}, element{N}, element{Ar} and element{He}, within their expected uncertainties, a result which is consistent with a flat or small abundance gradient in the Galactic disc within +/-2 kpc from the Sun, as suggested by some studies of the abundances in H Ii regions and B-type stars. The same set of homogeneously derived ionic abundances is also used to test the accuracy of the fractional ionization predicted by available grids of models for photoionized nebulae. Based on observations made with the Isaac Newton Telescope, operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.