We report the phase behaviour of aqueous dispersions of magnetic nanoparticles in the high-volume-fraction regime. Osmotic compression experiments are used to obtain high particle volume fractions in the range of low ionic strength. The suspensions exhibit a reversible rheological liquid—solid transition for a given particle volume fraction. The threshold of the transition is shifted towards low volume fractions by a decrease in the ionic strength. The structure factor of the suspensions obtained from small-angle neutron scattering measurements shows that the sum of the interactions in the system is dominated by strong electrostatic repulsions and that the suspensions exhibit a liquidlike structure even in the solid phase. The polydispersity of the system does not allow the crystal phase to be reached; the solid phase is thus a Wigner glass. The threshold of the transition is consistent with the theoretical threshold of a solid transition for a system of hard spheres, taking for the radius of the particle an effective radius: the sum of the radius and the Debye length. Repulsions are so efficient that the sum of the interactions remains isotropic under the appliance of a magnetic field. It is nevertheless possible to induce a solid-liquid transition by the appliance of a magnetic field.