M subdwarfs are metal poor and cool stars. They are important probes of the old galactic populations. However, they remain elusive due to their low luminosity. Observational and modeling efforts are required to fully understand their physics and to investigate the effects of metallicity in their cool atmospheres. We perform a detailed study of a sample of subdwarfs to determine their stellar parameters and constrain the stat-of-the art atmospheric models. We present UVES/VLT high resolution spectra of three late-K subdwarfs and 18 M subdwarfs. Our atlas covers the optical region from 6400{AA} up to the near infrared at 8900{AA}. We show spectral details of cool atmospheres at very high resolution (R~40000) and compare with synthetic spectra computed from the recent BT-Settl atmosphere models. Our comparison shows that molecular features (TiO, VO, CaH), and atomic features (FeI, TiI, NaI, KI) are well fitted by current models. We produce an effective temperature versus spectral type relation all over the subdwarf spectral sequence. Thanks to the high resolution of our spectra, we perform a detailed comparison of line profiles of individual elements such as FeI, CaII, TiI, and are able to determine accurate metallicities of these stars. These determinations contribute to calibrate the relation between metallicity and molecular band strength indices from low-resolution spectra. This work shows that the new generation of models are able to reproduce various spectral features of M subdwarfs. Working with these high resolution spectra allowed us to disentangle the atmospheric parameters (effective temperature, gravity, metallicity), which is not possible when using low resolution spectroscopy or photometry.