Unmanned aerial vehicles (UAV) are increasingly becoming a popular tool in the observation and study of marine mammals. However, the potential capabilities of these vehicles regarding autonomous operations are not being fully exploited for passive underwater acoustic monitoring in marine mammal research. This article presents results from the development of a UAV system equipped with an underwater acoustic recorder aimed at assisting with the monitoring of harbour porpoises in Special Areas of Conservation in the United Kingdom. The UAV is capable of autonomous navigation, persistent landing, take-off and automatic data acquisition at specified waypoints. The system architecture that enables autonomous UAV flight including waypoint planning and control is described. A bespoke lightweight underwater acoustic recorder (named the PorpDAQ) capable of transmitting the results of fast Fourier transforms (FFT) applied to incoming signals from a hydrophone was also designed. The system’s operation is successfully validated with a combination of outdoor experiments and indoor simulations demonstrating different UAVs capable of autonomously navigating and landing at specific waypoints while recording data in an indoor tank. Results from the recorder suggest that lightweight, relatively low-cost systems can be used in place of heavier more expensive alternatives.