High-speed obstacle avoidance of uncrewed aerial vehicles (UAVs) in cluttered environments is a significant challenge. Existing UAV planning and obstacle avoidance systems can only fly at moderate speeds or at high speeds over empty or sparse fields. In this article, we propose a hyper-efficient perception and planning system for the high-speed obstacle avoidance of UAVs. The system mainly consists of three modules: 1) A novel incremental robocentric mapping method with distance and gradient information, which takes 89.5% less time compared to existing methods. 2) A novel obstacle-aware topological path search method that generates multiple distinct paths. 3) An adaptive gradient-based high-speed trajectory generation method with a novel time pre-allocation algorithm. With these innovations, the system has an excellent real-time performance with only milliseconds latency in each iteration, taking 79.24% less time than existing methods at high speeds (15 m/s in cluttered environments), allowing UAVs to fly swiftly and avoid obstacles in cluttered environments. The planned trajectory of the UAV is close to the global optimum in both temporal and spatial domains. Finally, extensive validations in both simulation and real-world experiments demonstrate the effectiveness of our proposed system for high-speed navigation in cluttered environments.