This paper proposes a non-linear Model Predictive Contouring Control (MPCC) for obstacle avoidance in automated vehicles driven at the limit of handling. The proposed controller integrates motion planning, path tracking and vehicle stability objectives, prioritising obstacle avoidance in emergencies. The controller's prediction model is a non-linear single-track vehicle model with the Fiala tyre to capture the vehicle's non-linear behaviour. The MPCC computes the optimal steering angle and brake torques to minimise tracking error in safe situations and maximise the vehicle-to-obstacle distance in emergencies. Furthermore, the MPCC is extended with the tyre friction circle to fully exploit the vehicle's manoeuvrability and stability. The MPCC controller is tested using real-time rapid prototyping hardware to prove its real-time capability. The performance is compared with a state-of-the-art Model Predictive Control (MPC) in a high-fidelity simulation environment. The double lane change scenario results demonstrate a significant improvement in successfully avoiding obstacles and maintaining vehicle stability.