Context. We aim to understand the accretion history of the Milky Way by exploring the vertical and radial properties of the Galactic thick disc. Aims: We study the chemical and kinematic properties of roughly a thousand spectra of faint magnitude foreground Galactic stars observed serendipitously during extra-galactic surveys in four lines-of-sight: three in the southern Galactic hemisphere (surveys of the Carina, Fornax and Sculptor dwarf spheroidal galaxies) and one in the northern Galactic hemisphere (a survey of the Sextans dwarf spheroidal galaxy). The foreground stars span distances up to ~3 kpc from the Galactic plane and Galactocentric radii up to 11 kpc. Methods: The stellar atmospheric parameters (effective temperature, surface gravity, metallicity) are obtained by an automated parameterisation pipeline and the distances of the stars are then derived by a projection of the atmospheric parameters on a set of theoretical isochrones using a Bayesian approach. The metallicity gradients are estimated for each line-of-sight and compared with predictions from the Besançon model of the Galaxy, in order to test the chemical structure of the thick disc. Finally, we use the radial velocities in each line-of-sight to derive a proxy for either the azimuthal or the vertical component of the orbital velocity of the stars. Results: Only three lines-of-sight have a sufficient number of foreground stars for a robust analysis. Towards Sextans in the Northern Galactic hemisphere and Sculptor in the South, we measure a consistent decrease in mean metallicity with height from the Galactic plane, suggesting a chemically symmetric thick disc. This decrease can either be due to an intrinsic thick disc metallicity gradient, or simply due to a change in the thin disc/thick disc population ratio and no intrinsic metallicity gradients for the thick disc. We favour the latter explanation. In contrast, we find evidence of an unpredicted metal-poor population in the direction of Carina. This population was earlier detected, but our more detailed analysis provides robust estimates of its location (|Z| < 1 kpc), metallicity (-2 < [M/H] < -1 dex) and azimuthal orbital velocity (Vφ ~ 120 km s-1). Conclusions: Given the chemo-dynamical properties of the over-density towards the Carina line-of-sight, we suggest that it represents the metal-poor tail of the canonical thick disc. In spite of the small number of stars available, we suggest that this metal-weak thick disc follows the often suggested canonical thick disc velocity-metallicity correlation of ∂Vφ/∂ [M/H] ~ 40-50 km s-1 dex-1. Based on observations collected at the European Southern Observatory at Paranal, Chile, ESO Large Programme 171.B-0588 (DART) and 171.B-0520(A).Full Tables 2 and 4 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/555/A12