Predictably, future urban airspaces will be crowded with autonomous unmanned aerial vehicles (UAVs) offering different services to the population. One of the main challenges in this new scenario is the design of collision-free navigation algorithms to avoid conflicts between flying UAVs. The most appropriate collision avoidance strategies for this scenario are non-centralized ones that are dynamically executed (in real time). Existing collision avoidance methods usually entail a high computational cost. In this work, we present Bounding Box Collision Avoidance (BBCA) algorithm, a simplified velocity obstacle-based technique that achieves a balance between efficiency and cost. The performance of the proposal is analyzed in detail in different airspace configurations. Simulation results show that the method is able to avoid all the conflicts in two UAV scenarios and most of them in multi-UAV ones. At the same time, we have found that the penalty of using the BBCA collision avoidance technique on the flying time and the distance covered by the UAVs involved in the conflict is reasonably acceptable. Therefore, we consider that BBCA may be an excellent candidate for the design of collision-free navigation algorithms for UAVs.