Hybrid planner switching framework (HPSF) for autonomous driving needs to reconcile high-speed driving efficiency with safe maneuvering in dense traffic. Existing HPSF methods often fail to make reliable mode transitions or sustain efficient driving in congested environments, owing to heuristic scene recognition and low-frequency control updates. To address the limitation, this paper proposes LAP, a large language model (LLM) driven, adaptive planning method, which switches between high-speed driving in low-complexity scenes and precise driving in high-complexity scenes, enabling high qualities of trajectory generation through confined gaps. This is achieved by leveraging LLM for scene understanding and integrating its inference into the joint optimization of mode configuration and motion planning. The joint optimization is solved using tree-search model predictive control and alternating minimization. We implement LAP by Python in Robot Operating System (ROS). High-fidelity simulation results show that the proposed LAP outperforms other benchmarks in terms of both driving time and success rate.