The problem of natural language to visualisation (NL2VIS) has gained much attention worldwide, especially among non-technical people. Large language models (LLMs) are widely studied and applied in this field because of their ability to understand diverse semantics. However, previous studies still face many limitations in learning appropriate communication with LLMs, leading to the need to learn a new skill called prompt engineering. To address the above challenge, this study introduces IntelliChart - a full query-to-visualization cycle. IntelliChart decomposes the NL2VIS process into modular sub-tasks, integrating LLMs with state management. This design combines query validation, agent-based SQL execution, insight extraction and visualization generation, enhanced by retry logic and interpretation services. The study is evaluated both qualitatively and quantitatively. Qualitative results showed that IntelliChart allows for more explicit interpretation of results than ChatGPT. Quantitative results on the VisEval dataset showed that IntelliChart achieves 51.2% Exact Match accuracy and 99.8% Execution Success rate, outperforming baselines including hybrid frameworks, pipelined methods, and naive LLM prompts. This research will contribute to enriching the NL2VIS experimental literature, thereby paving the way for more reliable data visualization systems. The repository is available at: https://github.com/ictu-se/IntelliChart.