This paper proposes a linear predictive lateral control method to stabilise a highly automated vehicle (HAV) at the tire-road friction limits when tracking a (tight) desired path. Two approaches are adopted to linearise the vehicle model around the tire saturation region: (1) the lateral force of the front tire is selected as the control input instead of the steer angle and (2) the rear tire dynamics is locally linearised at the current operating point within the predictive horizon. The friction limits of both the front and rear tires are utilised to define an enveloped stable zone, which serves as the safety constraints for the predictive controller. Simulation results show that the proposed controller is able to stabilise a vehicle when tracking a tight desired path at a high speed even on a low-adhesion road. Moreover, the robustness of the proposed controller is also verified as it tolerates small estimation errors in the road friction coefficient.