Large Language Models (LLMs) offer promising opportunities for automating online extremism detection, yet challenges remain in capturing nuanced rhetoric and complex social dynamics. In this study, we evaluate state-of-the-art LLMs (GPT-4o, LLaMA, Gemini, and Mixtral) using the updated UK government definition of extremism, analysing 500 user examples. GPT-4o notably achieved an accuracy of 80% in extremism detection with a Macro-F1 score of 71%. Fine-tuned approaches similarly produced 82% accuracy and 82% Macro-F1. However, performance dropped significantly when distinguishing nuanced social roles, particularly within contexts characterised by complex emotional tones or negative sentiment. These findings highlight both the strengths and current limitations of LLMs in automated content moderation, pointing to critical areas for further improvement in the analysis of extremist discourse.