One of the challenges in robotics is to enable robotic units with the reasoning capability that would be robust enough to execute complex tasks in dynamic environments. Recent advances in LLMs have positioned them as go-to tools for simple reasoning tasks, motivating the pioneering work of Liang et al. [35] that uses an LLM to translate natural language commands into low-level static execution plans for robotic units. Using LLMs inside robotics systems brings their generalization to a new level, enabling zero-shot generalization to new tasks. This paper extends this prior work to dynamic environments. We propose InCoRo, a system that uses a classical robotic feedback loop composed of an LLM controller, a scene understanding unit, and a robot. Our system continuously analyzes the state of the environment and provides adapted execution commands, enabling the robot to adjust to changing environmental conditions and correcting for controller errors. Our system does not require any iterative optimization to learn to accomplish a task as it leverages in-context learning with an off-the-shelf LLM model. Through an extensive validation process involving two standardized industrial robotic units -- SCARA and DELTA types -- we contribute knowledge about these robots, not popular in the community, thereby enriching it. We highlight the generalization capabilities of our system and show that (1) in-context learning in combination with the current state-of-the-art LLMs is an effective way to implement a robotic controller; (2) in static environments, InCoRo surpasses the prior art in terms of the success rate; (3) in dynamic environments, we establish new state-of-the-art for the SCARA and DELTA units, respectively. This research paves the way towards building reliable, efficient, intelligent autonomous systems that adapt to dynamic environments.