This paper explores how the critical learning dimension in an English for academic purposes (EAP) programme in a British university is developed in the context of one classroom task. The focus is on the speaking element of the activity which requires students in pairs to explore each other's personal language history (PLH), present the account to the class as a whole, and finally write it up in an academic style as homework. Ethnographic observation and interview data are used to describe the task process in the classroom and the teacher's and students' views of it. The pedagogical features of the activity are situated in the programme as a whole, i.e. the institutional specification and the teacher's introduction in the first session. The learning goals of both the programme and the task are related to current debates on pragmatic and critical approaches in EAP. The classroom and interview data are analysed using a framework for critical learning developed by Robert Young [Critical theory and classroom talk. Clevedon: Multilingual Matters, 1992]. The conclusion discusses the nature and process of critical learning as evidenced by the PLH task, the role of speaking in the development of the critical faculty in the EAP classroom, and how pedagogical approaches in relation to these might benefit from further evaluation and research.