Unmanned Aerial Vehicles (UAVs) are being increasingly implemented in a range of applications. Their low payload capacity and ability to overcome congested road networks enables them to provide fast delivery services for urgent high-value low-volume cargo. This work investigates the economic viability of integrating UAVs into urban hospital supply chains. In doing so, a strategic model that determines the optimal configuration of supporting infrastructure for urgent UAV delivery between hospitals is proposed. The model incorporates a tailored facility location algorithm that selects an optimal number of hubs given a set of candidates and determines the number of UAVs required to fulfil total demand. The objective is to minimize the total cost of implementation, computed as the sum of generalised, battery, vehicle and hub establishment costs. The model is applied to a case study based on the establishment of a UAV delivery network for deliveries between NHS hospitals in London. A baseline scenario is also developed using current NHS vehicles for delivery. Our results demonstrate that UAV-based delivery provide significant reductions in operational costs compared to the baseline. Furthermore, our analysis indicates the location of hubs is more significant to the solution optimality than any increase in range or payload.