Depletion interactions give rise to phase separation in colloid-polymer mixtures at sufficiently high concentrations of both species. Similarly a fluid-solid phase separation is expected for binary hard sphere (BHS) mixtures, however in practice it appears such mixtures are very prone to form metastable (jammed) states. Here pNIPAM microgel particles are used to induce depletion attractions between polystyrene latex spheres. Such microgels can be modelled as hard spheres with a polymer brush-like outer layer. Mixtures with a microgel/polystyrene size ratio of 0.11 showed a fluid-solid phase separation, in good agreement with predictions for BHS. Gel states were obtained on further increase of concentration, around the position of the predicted metastable BHS fluid-fluid binodal, echoing previous claims of the significance of a hidden fluid-fluid phase boundary as the precursor to gelation. It thus appears that the slight deformability of the microgel particles reduces the tendency for mixtures to remain in jammed states relative to binary hard sphere systems. Nevertheless the mixtures did tend to form gels more easily than mixtures of the same polystyrene spheres with linear polymer coils at a similar polymer/colloid size ratio.