Abstract Using the astrometry from the ESA’s Gaia mission, previous works have shown that the Milky Way stellar halo is dominated by metal-rich stars on highly eccentric orbits. To shed light on the nature of this prominent halo component, we have analysed 28 Galaxy analogues in the Auriga suite of cosmological hydrodynamics zoom-in simulations. Some three quarters of the Auriga galaxies contain prominent components with high radial velocity anisotropy, β > 0.6. However, only in one third of the hosts do the high-β stars contribute significantly to the accreted stellar halo overall, similar to what is observed in the Milky Way. For this particular subset we reveal the origin of the dominant stellar halo component with high metallicity, [Fe/H] ∼ −1, and high orbital anisotropy, β > 0.8, by tracing their stars back to the epoch of accretion. It appears that, typically, these stars come from a single dwarf galaxy with a stellar mass of the order of $10^9-10^{10}\, {\rm M}_⊙$ that merged around $6-10 \, {\rm Gyr}$ ago, causing a sharp increase in the halo mass. Our study therefore establishes a firm link between the excess of radially anisotropic stellar debris in the halo and an ancient head-on collision between the young Milky Way and a massive dwarf galaxy.