The European Union (Withdrawal) Act 2018 forms the centrepiece of the UK's domestic legal preparations for its departure from the European Union. The Act aims to capture and domesticate large swathes of EU law so as to safeguard legal continuity upon Brexit. This paper examines the process by which the Act was passed by the UK Parliament and its substantive constitutional implications, which are likely to be far-reaching. Membership of the EU has had a monumental impact not only upon the substantive law of the UK, but also upon the development of fundamental constitutional doctrines, principles and practices over more than four decades, affecting our understanding of parliamentary supremacy, the relationship between Parliament and Government, the constitutional authority of the courts and the creation and development of devolved government. The implications of the Act go far beyond the immediate task of retaining and reordering the domestic effect of EU law. The paper assesses the deeper consequences which the Act signifies for four dimensions of the constitution: the rule of law and legal certainty, parliamentary supremacy, the relationship between Parliament and government, and the UK's territorial constitution.