Planning algorithms decompose complex problems into intermediate steps that can be sequentially executed by robots to complete tasks. Recent works have employed Large Language Models (LLMs) for task planning, using natural language to generate robot policies in both simulation and real-world environments. LLMs like GPT-4 have shown promising results in generalizing to unseen tasks, but their applicability is limited due to hallucinations caused by insufficient grounding in the robot environment. The robustness of LLMs in task planning can be enhanced with environmental state information and feedback. In this paper, we introduce a novel approach to task planning that utilizes two separate LLMs for high-level planning and low-level control, improving task-related success rates and goal condition recall. Our algorithm, \textit{BrainBody-LLM}, draws inspiration from the human neural system, emulating its brain-body architecture by dividing planning across two LLMs in a structured, hierarchical manner. BrainBody-LLM implements a closed-loop feedback mechanism, enabling learning from simulator errors to resolve execution errors in complex settings. We demonstrate the successful application of BrainBody-LLM in the VirtualHome simulation environment, achieving a 29\% improvement in task-oriented success rates over competitive baselines with the GPT-4 backend. Additionally, we evaluate our algorithm on seven complex tasks using a realistic physics simulator and the Franka Research 3 robotic arm, comparing it with various state-of-the-art LLMs. Our results show advancements in the reasoning capabilities of recent LLMs, which enable them to learn from raw simulator/controller errors to correct plans, making them highly effective in robotic task planning.