The authors investigate the Einstein equation for a class of (4n+4)-dimensional SU(2)-invariant metrics on S⁴ and R⁴ fibre bundles over quaternionic Kahler base manifolds. Using numerical techniques, they establish the existence of complete compact inhomogeneous Einstein spaces of this form with positive Ricci curvature, and complete non-compact inhomogeneous Einstein spaces with zero or negative Ricci curvature.