The effect of EU law on UK insolvencies is, as a general rule, limited to cross-border issues. Within the EU, the EC Regulation on Insolvency Proceedings governs all the main jurisdictional and choice of law questions that arise in international insolvencies (with the exception of the insolvencies of banks, insurers and certain investment companies).
In particular, the EC Regulation provides for the recognition of insolvency proceedings opened in one Member State by the courts of the others. When the UK leaves the EU, the EC Regulation will cease to apply. Unless some alternative arrangements are put in place (and it seems unlikely that that will be a diplomatic priority in the years ahead), the main result will be that UK insolvency officeholders will no longer be entitled to automatic recognition in EU countries – making cross-border insolvencies more complex and expensive.