Context. Iron plays a crucial role in studies of late-type stars. In their atmospheres, neutral iron is the minority species and lines of Fe i are subject to the departures from LTE. In contrast, one believes that LTE is a realistic approximation for Fe ii lines. The main source of the uncertainties in the non-local thermodynamic equilibrium (non-LTE = NLTE) calculations for cool atmospheres is a treatment of inelastic collisions with hydrogen atoms. Aims. We investigate the effect of Fe i + H i and Fe ii + H i collisions and their different treatment on the Fe i/Fe ii ionisation equilibrium and iron abundance determinations for Galactic halo benchmark stars HD 84937, HD 122563, and HD 140283 and a sample of 38 very metal-poor (VMP) giants in the dwarf galaxies with well known distances. Methods. We perform the NLTE calculations for Fe i -Fe ii with applying quantum-mechanical rate coefficients for collisions with H i from Barklem (2018, B18), Yakovleva, Belyaev, and Kraemer (2018, YBK18), and Yakovleva, Belyaev, and Kraemer (2019, YBK19). Results. We find that collisions with H i serve as efficient thermalisation processes for Fe ii, such that the NLTE abundance corrections for Fe ii lines do not exceed 0.02 dex, in absolute value, at [Fe/H] −3 and reach +0.06 dex at [Fe/H] ∼ −4. For a given star, different treatments of Fe i + H i collisions by B18 and YBK18 lead to similar average NLTE abundances from the Fe i lines, although there exist discrepancies in the NLTE abundance corrections for individual lines. With using quantum-mechanical collisional data and the Gaia based surface gravity, we obtain consistent abundances from the two ionisation stages, Fe i and Fe ii, for a red giant HD 122563. For a turn-off star HD 84937 and a subgiant HD 140283, we analyse the iron lines in the visible and the ultra-violet (UV, 1968 to 2990 Å) range. For either Fe i or Fe ii, abundances from the visible and UV lines are found to be consistent in each star. The NLTE abundances from the two ionisation stages agree within 0.10 dex, when using the YBK18 data, and 0.13 dex in case of B18. The Fe i/Fe ii ionisation equilibrium is achieved for each star of our stellar sample in the dwarf galaxies, with the exception of stars at [Fe/H] −3.7.