Phishing has become a prominent risk in modern cybersecurity, often used to bypass technological defences by exploiting predictable human behaviour. Warning dialogues are a standard mitigation measure, but the lack of explanatory clarity and static content limits their effectiveness. In this paper, we report on our research to assess the capacity of Large Language Models (LLMs) to generate clear, concise, and scalable explanations for phishing warnings. We carried out a large-scale between-subjects user study (N = 750) to compare the influence of warning dialogues supplemented with manually generated explanations against those generated by two LLMs, Claude 3.5 Sonnet and Llama 3.3 70B. We investigated two explanatory styles (feature-based and counterfactual) for their effects on behavioural metrics (click-through rate) and perceptual outcomes (e.g., trust, risk, clarity). The results indicate that well-constructed LLM-generated explanations can equal or surpass manually crafted explanations in reducing susceptibility to phishing; Claude-generated warnings exhibited particularly robust performance. Feature-based explanations were more effective for genuine phishing attempts, whereas counterfactual explanations diminished false-positive rates. Other variables such as workload, gender, and prior familiarity with warning dialogues significantly moderated warning effectiveness. These results indicate that LLMs can be used to automatically build explanations for warning users against phishing, and that such solutions are scalable, adaptive, and consistent with human-centred values.