This paper investigates the application of pre-trained large language models (LLMs) for spam email classification using zero-shot prompting. We evaluate the performance of both open-source (Flan-T5) and proprietary LLMs (ChatGPT, GPT-4) on the well-known SpamAssassin dataset. Two classification approaches are explored: (1) truncated raw content from email subject and body, and (2) classification based on summaries generated by ChatGPT. Our empirical analysis, leveraging the entire dataset for evaluation without further training, reveals promising results. Flan-T5 achieves a 90% F1-score on the truncated content approach, while GPT-4 reaches a 95% F1-score using summaries. While these initial findings on a single dataset suggest the potential for classification pipelines of LLM-based subtasks (e.g., summarisation and classification), further validation on diverse datasets or multilingual scenarios is necessary. Besides, the high operational costs of proprietary models, coupled with the general inference costs of LLMs, could significantly hinder real-world deployment for spam filtering.