ABSTRACT We study the orbital phase space of dark matter (DM) haloes in the auriga suite of cosmological hydrodynamics simulations of Milky Way (MW) analogues. We characterize haloes by their spherical action distribution, $F\left(J_{{r}},L\right)$, a function of the specific angular momentum, L, and the radial action, Jr, of the DM particles. By comparing DM-only and hydrodynamical simulations of the same haloes, we investigate the contraction of DM haloes caused by the accumulation of baryons at the centre. We find a small systematic suppression of the radial action in the DM haloes of the hydrodynamical simulations, suggesting that the commonly used adiabatic contraction approximation can result in an underestimate of the density by $∼ 8{{ \rm {per\ cent}}}$. We apply an iterative algorithm to contract the auriga DM haloes given a baryon density profile and halo mass, recovering the true contracted DM profiles with an accuracy of $∼ 15{{ \rm {per\ cent}}}$, that reflects halo-to-halo variation. Using this algorithm, we infer the total mass profile of the MW’s contracted DM halo. We derive updated values for the key astrophysical inputs to DM direct detection experiments: the DM density and velocity distribution in the Solar neighbourhood.