We present a homogeneous set of accurate atmospheric parameters for a complete sample of very and extremely metal-poor stars in the dwarf spheroidal galaxies (dSphs) Sculptor, Ursa Minor, Sextans, Fornax, Botes I, Ursa Major II, and Leo IV. We also deliver a Milky Way (MW) comparison sample of giant stars covering the 4 < [Fe /H] < 1 : 7 metallicity range. We show that, in the [Fe /H] greater than or similar to 3 : 7 regime, the non-local thermodynamic equilibrium (NLTE) calculations with non-spectroscopic effective temperature (T-eff) and surface gravity (log(g)) based on the photometric methods and known distance provide consistent abundances of the Fei and Feii lines. This justifies the Fei/Feii ionisation equilibrium method to determine logg for the MW halo giants with unknown distance. The atmospheric parameters of the dSphs and MW stars were checked with independent methods. In the [Fe /H] > 3 : 5 regime, the Tii/Tiii ionisation equilibrium is fulfilled in the NLTE calculations. In the logg T-eff plane, all the stars sit on the giant branch of the evolutionary tracks corresponding to [Fe /H] = 2 to 4, in line with their metallicities. For some of the most metal-poor stars of our sample, we achieve relatively inconsistent NLTE abundances from the two ionisation stages for both iron and titanium. We suggest that this is a consequence of the uncertainty in the T-eff-colour relation at those metallicities. The results of this work provide the basis for a detailed abundance analysis presented in a companion paper.