Context. Representative samples of F-, G-, K-type stars located outside of the solar neighbourhood have started to become available in spectroscopic surveys. The fraction of metal-poor ([Fe/H] ≲ −0.8 dex) giants becomes increasingly relevant towards greater distances. In metal-poor stars, effective temperatures (Teff) based on local thermodynamic equilibrium (LTE) spectroscopy and on former colour–Teff relations – which are still widely used – have been reported to be inaccurate. It is necessary to recalibrate chemical abundances based on these Teff scales in the multiple available surveys in order to bring them to the same standard scale for their simultaneous use. To this end, a complete sample of standards is required, which until now has been restricted to a few stars with quasi-direct Teff measurements. Aims. We aim to provide a legacy sample of metal-poor standards with proven accurate atmospheric parameters. We add 47 giants to the TITANS metal-poor reference stars. Methods. We derived Teff using 3D non-LTE Hα modelling, the accuracy of which was tested against interferometry and with the Infra Red Flux Method (IRFM). We derived surface gravity (log ɡ) by fitting Mg I b triplet lines, and tested their accuracy against asteroseismology. Metallicity was derived using Fe II lines, and we find our results to be identical to the [Fe/H] derived from non-LTE spectral synthesis. Results. The Teff that we find using 3D non-LTE Hα is equivalent to interferometric and IRFM temperatures within a ±46 K uncertainty. We achieve precision of ~50 K for 34 stars with spectra with the highest signal-to-noise ratio (S/N). For log ɡ, we achieve a total uncertainty of ±0.15 dex. For [Fe/H], we obtain a total uncertainty of ±0.09 dex. We find that the ionisation equilibrium of Fe lines under LTE is not valid in metal-poor giants. LTE leads to a small but significant metallicity underestimation of ~0.1 dex when derived from weak Fe I lines, and only provided accurate Teff and log ɡ. This bias totally disappears under non-LTE.