In this paper we propose a new vision-based obstacle avoidance strategy using the Underwater Dark Channel Prior (UDCP) that can be applied to any Unmanned Underwater Vehicle (UUV) equipped with a simple monocular camera and minimal on-board processing capabilities. For each incoming image, our method first computes a relative depth map to estimate the obstacles nearby. Then, the map is segmented and the most promising Region of Interest (RoI) is identified. Finally, an escape direction is computed within the RoI and a control action is performed accordingly to avoid the obstacles. We tested our approach on a video sequence in a natural environment and compared it against a state-of-the-art method showing better performance, specially in light changing conditions. We also provide online results on a low-cost Remotely Operated Vehicle (ROV) in a controlled environment.