Brexit & EIP
EU law currently applies in the UK through the direct effect of Regulations. If this law is to continue to apply these Regulations would need to be transposed into UK law. It is inevitably the case that sometimes there will be differences in language between the source Regulation and UK legislation enacted to mirror its effect that may result in legal arguments as to the scope of the new legislation. Moreover, when any legislation is to be adopted, Parliament will have the opportunity to debate and amend the proposals. There is no guarantee that a post-Brexit parliament would not amend the impact of an EU Regulation.
As well as EU Regulations (which take effect in EU Member States directly), a significant proportion of EU law requires each EU Member State to implement national legislation to reflect the articles and purposes of EU Directives. UK legislation that has been enacted to implement EU Directives will, by default, remain part of UK law even after Brexit. It seems likely that a post-Brexit UK government will want to review the body of UK laws that stems from EU Directives. This leaves the status of that legislation uncertain.
The application of a law is not simply the words of a statute. These words are brought to life by the court applying them. The UK Courts currently interpret law emanating from the EU in line with (a) the purpose of the underlying EU legislation, including taking account of the travaux préparatoires associated with the underlying purposes of the EU legislators; and (b) case law of the Court of Justice of the European Union ruling on how that legislation should be implemented and interpreted. It seems unlikely that a post-Brexit UK government would generally continue to require that UK law be interpreted in line with EU jurisprudence.