Whilst the Companies Act 2006 and the raft of secondary legislation made under it have been heavily influenced by various European Directives (notably the Company Law Directives and Accounting Directives and the Shareholder Rights Directive), it is unlikely that the Companies Act would be an area of immediate priority for overhaul, should the UK leave the EU.
There may be some attempt to remove any unnecessary burdens on business which were previously derived from European Directives. However, given the history of the Companies Acts in the UK, and the extensive consultation process which gave rise to the Companies Act 2006 itself, the key features of company law, including the types of companies which can be incorporated, the role of Companies House as Registrar, directors' duties and shareholder remedies, and the rules on accounts and audit would be expected to remain generally the same.
UK companies with subsidiaries incorporated in the rest of the EU or companies in the EU with subsidiaries in the UK may experience new challenges running their groups cross-border over time, should the EU and UK company law frameworks diverge.
European companies with a registered UK establishment in the UK should expect no immediate change – the rules relating to UK establishments currently apply equally to companies in and outside the EU. UK companies with establishments/branches (so not companies/subsidiaries) in other EU Member States should probably not expect any immediate change, unless their regulatory framework is affected (see the Financial services regulation section), although challenges may increase over time, should the EU and UK company law frameworks diverge.