In this work, we combine spectroscopic information from the SkyMapper survey for Extremely Metal-Poor stars and astrometry from Gaia DR2 to investigate the kinematics of a sample of 475 stars with a metallicity range of -6.5<=[Fe/H]<=-2.05dex. Exploiting the action map, we identify 16 and 40 stars dynamically consistent with the Gaia Sausage and Gaia Sequoia accretion events, respectively. The most metal poor of these candidates have metallicities of [Fe/H]=-3.31 and -3.74, respectively, helping to define the low-metallicity tail of the progenitors involved in the accretion events. We also find, consistent with other studies, that ~21 per cent of the sample have orbits that remain confined to within 3kpc of the Galactic plane, that is, |Z_max_|<=3kpc. Of particular interest is a subsample (~11 per cent of the total) of low |Z_max_| stars with low eccentricities and prograde motions. The lowest metallicity of these stars has [Fe/H]=-4.30 and the subsample is best interpreted as the very low-metallicity tail of the metal-weak thick disc population. The low |Z_max_|, low eccentricity stars with retrograde orbits are likely accreted, while the low |Z_max_|, high eccentricity pro- and retrograde stars are plausibly associated with the Gaia Sausage system. We find that a small fraction of our sample (~4 per cent of the total) is likely escaping from the Galaxy, and postulate that these stars have gained energy from gravitational interactions that occur when infalling dwarf galaxies are tidally disrupted.