Professor Arnull's research has focused mainly on the law of the European Union, in particular the role and jurisdiction of the European Court of Justice; the configuration of the European Union's judicial system; and the relationship between European Union law and national law, especially that of the United Kingdom. His monograph on the European Court of Justice, now in its second edition, has been described as ‘an excellent book…useful, well-conceived and thoroughly well-executed…’
His recent work has examined the response of the Member States to decisions of the European Court of Justice perceived as ‘activist’; the changing style of scholarship on European Union law; the approach of the Appellate Committee of the House of Lords to European Union law; the process which led to the Treaty of Lisbon and the various crises by which that process was punctuated; the events surrounding the ratification of the Treaty of Lisbon by Ireland; the principle of effective judicial protection in European Union law; the effect of the Treaty of Lisbon on the European Court of Justice; judicial dialogue in the European Union; and the role academics might play in responding to the case law of the European Court of Justice.