On 1 February 2020, the United Kingdom (UK) left the European Union (EU). After a transition period that ended on 31 December 2020, EU law instruments that applied to the UK, generally no longer applied. These legal instruments include directives such as the EU Dispute Resolution Directive. The EU and the UK have taken the position that the same applies to the EU Arbitration Convention, which is an instrument of international law entered into between Member States, but not an instrument of EU law. The authors analyse what the consequences of Brexit were for the EU Arbitration Convention and whether the joint position taken by the European Council and the UK can be supported under EU and international law.