  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, Bo\"otes 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] > -3.5 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 Fe I and Fe II lines. This justifies the Fe I/Fe
II 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 Ti I/Ti II
ionisation equilibrium is fulfilled in the NLTE calculations. In the log~g -
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.
