Emergency Medical Systems (EMSs) are an important component of public health-care services. Improving infrastructure for EMS and specifically the construction of base stations at the ”right” locations to reduce response times is the main focus of this paper. This is a computationally challenging task because of the: (a) exponentially large action space arising from having to consider combinations of potential base locations, which themselves can be significant; and (b) direct impact on the performance of the ambulance allocation problem, where we decide allocation of ambulances to bases. We present an incremental greedy approach to discover the placement of bases that maximises the service level of EMS. Using the properties of submodular optimisation we show that our greedy algorithm provides quality guaranteed solutions for one of the objectives employed in real EMSs. Furthermore, we validate our derived policy by employing a real-life event driven simulator that incorporates the real dynamics of EMS. Finally, we show the utility of our approaches on a real-world dataset from a large asian city and demonstrate significant improvement over the best known approaches from literature.