We present the results of calculations of the energy levels of defects at the (001) surface of MgO relative to the top of the valence band and values of defect ionisation potentials and electron affinities. The calculations were made using an embedded cluster method in which a cluster of several tens of ions treated quantum mechanically is embedded in a finite array of polarisable and point ions modelling the crystalline potential and the classical polarisation of the host lattice. The calculated ionisation potential of the ideal surface, which fixes the position of the top of the valence band with respect to the vacuum level, is about 6.7 eV. This value is used as a reference for positioning the energy levels of three charge states of a surface anion vacancy, which are also calculated as ionisation energies with respect to the vacuum level. The surface and vacancy electron affinities are calculated using the same method. As a prototype low-coordinated surface site, we have considered a cube corner. Our calculations predict the splitting of the corner states from the top of the surface valence band by about 1.0 eV. Both unrelaxed and relaxed holes are strongly localised at the corner oxygen ion. The ionisation energies and electron affinities of the corner anion vacancy are calculated. The electrons in the F and F + centres at the corner are shown to be significantly delocalised over surrounding Mg ions.