Within the fields of narratology, cognitive linguistics and political discourse analysis, this paper adopts a critical approach to narrative analysis in order to provide an empirical study of Brexit discourse. By doing so, we propose to contribute, modestly, to the prolific field of critical discourse analysis (CDA) by attempting to determine whether political storytelling elements, which we understand as comprehensive and independent narrative units, with a beginning, a middle and an end and some sort of implicit moral – and which are often discarded as mere anecdotes or irrelevant digressions – might constitute a credible driver of political persuasion. As such, our approach is thematic and our attention is on the interactional and social work that narrators do through stories and on the cognitive effects and consequences of narrative talk, which means that our research falls within one particular branch of narrative analysis, according to Mishler’s typology, whose study centres on the investigation of narrative functions in social contexts. Storytelling is a relatively old and polymorphous marketing technique, whose aim is to arouse interest and support by telling stories to audiences. We posit that the storytelling elements in any given political speech are purposeful, and when analysed critically and methodologically, they reveal the underlying narrative arc at work in the text, which arguably, plays a key role in the process of persuasion, as they contribute to the elaboration of worldviews and political ideologies. We will first clarify the rationale and explain why political storytelling represents a suitable candidate for CDA, mainly because of its cognitive and structural dimension. We will then specify how this approach can make a positive contribution to CDA thanks to a corpus-based analysis focusing on how Vote Leave’s pro-Brexit arguments were narrativized through storytelling.