It is becoming common practice to consider that the Stokes-Einstein relation D/T~ η -1 usually works for liquids above their melting temperatures although there is also experimental evidence for its failure. Here we investigate numerically this commonly-invoked assumption for simple liquid metals as well as for their liquid alloys. Using ab initio molecular dynamics simulations we show how entropy scaling relationships developed by Rosenfeld can be used to predict the conditions for the validity of the Stokes-Einstein relation in the liquid phase. Specifically, we demonstrate the Stokes-Einstein relation may break down in the liquid phase of some liquid alloys mainly due to the presence of local structural ordering as evidenced in their partial two-body excess entropies. Our findings shed new light on the understanding of transport properties of liquid materials and will trigger more experimental and theoretical studies since excess entropy and its two-body approximation are readily obtainable from standard experiments and simulations.