In June 2016, the United Kingdom voted in a referendum to leave the European Union (EU). The consequences of Brexit are wide-ranging, but, from a legal perspective, it will entail the repeal of the European Communities Act 1972. The UK government does not intend to repeal EU law which is in existence on exit day, but, in terms of the interpretation of retained law, decisions of the Court of Justice of the European Union (CJEU) will no longer be binding after Brexit. Nevertheless, s. 6(2) of the EU (Withdrawal) Act 2018 does allow the UK courts to continue to pay regard to EU law and decisions of the CJEU ‘so far as it is relevant to any matter before the court’. This article will consider the meaning of the phrase ‘ may have regard to anything…so far as it is relevant’. In empowering the courts to consider post-Brexit CJEU authority subject to the undefined criterion of relevancy, how is this power likely to be exercised? A comparison will be drawn with the treatment of Privy Council and the UK case law in Commonwealth courts following the abolition of the right of appeal to the Privy Council, with particular reference to the example of Australia. It will be argued that guidance may be obtained from the common law legal family which can help us predict the future relevance and persuasiveness of CJEU case law in the interpretation of retained EU private law.