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, Bootes 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]=>-3.7 regime, the non-local thermodynamic equilibrium (NLTE) calculations with non-spectroscopic effective temperature (Teff) 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 log g 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-Teff 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 hardly achieve consistent NLTE abundances from the two ionisation stages for both iron and titanium. We suggest that this is a consequence of the uncertainty in the Teff-colour relation at those metallicities. The results of these work provide the base for a detailed abundance analysis presented in a companion paper.