Delivery drones are a disruptive technology that is spurring logistics system change, such as the adoption of urban micro-fulfilment centres (MFCs). In this paper, we develop and implement a two-stage continuum approximation (CA) model of this disruptive system in a geographic information system (GIS). The model includes common CA techniques at a local level to minimise cost, and then these local solutions are used in a second stage regional location-allocation multiple knapsack problem. We then compare the drone MFC system to a traditional delivery-by-truck system and investigate potential cost or emissions savings by adjusting time-window demand, logistical sprawl, electric truck alternatives, and MFC emissions. Furthermore, we conduct a sensitivity analysis to show that uncertainty in demand and effective storage density both significantly influence the number of MFCs selected and benchmark our model against commercial solvers. This methodology may also be further developed and applied to other new delivery vehicle modes.