Recent results have suggested that online Model Predictive Control (MPC) can be computed quickly enough to control fast sampled systems. High-speed applications impose a hard real-time constraint on the solution of the MPC problem, which generally prevents the computation of the optimal controller. In current approaches guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC scheme based on robust MPC design that recovers these guarantees while allowing for extremely fast computation. We show that a simple warm-start optimization procedure providing an enhanced feasible solution guarantees feasibility and stability for arbitrary time constraints. The proposed method can be practically implemented and efficiently solved for dynamic systems of significant problem size. Implementation details for a real-time robust MPC method are provided that achieves computation times equal to those reported for methods without guarantees. A 12-dimensional problem with 3 control inputs and a prediction horizon of 10 time steps is solved in 2msec with a performance deterioration less than 1% and thereby allows for sampling rates of 500Hz.