Online social media platforms have become a major place where people also discuss their opinions and express their feelings about socio-political phenomena such as elections and referendums. Human-generated online content is a fruitful resource for a deeper understanding of these happenings. In this study, we present a dataset comprising 45 months (from January 2016 until September 2019) of long-running discussions on Twitter about the Brexit referendum, which can be used by social scientists and journalists for understanding the evolution of the public debate about the phenomenon. This dataset comprises 50.8 million tweets and 3.97 million users, and is also enriched with additional meta-data attributes: bot score of users, sentiment information detected by our sentiment analyzer, political stance information predicted by our stance classifier. Considering all Brexit related tweets of users during our time period, we also determine their overall stance and sentiment.