As said in the linked article, UK’s laws have not changed yet. We would give the same advice to businesses: keep calm, nothing changes immediately.
The European Communities Act 1972 remains in force, as does all other EU legislation and UK implementing legislation. From what the political experts are saying, negotiations for leaving are likely to take at least two years, during which this legislation will remain in force.
When the UK does finally leave, we do not know which of the possible connections with the EU will be adopted therefore we do not know which EU inspired legislation will remain in force. And whatever option is chosen, the UK’s legislation implementing EU laws will remain in force until repealed.
When things do start to change, we certainly recommend that you keep an eye on legal developments – when negotiations crystallise into new arrangements, if you are in business you will need to remain up to date on the law. When concrete developments occur, our blog will include summaries of relevant changes. And if you're a registered member of our elXtr online DIY law platform, you can also access our suite of additional self-help materials which will be amended as the legal situation develops.
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In a bid to clear things up, Citizens Advice has put up a ‘Brexit - how it affects you’ post, which essentially points out that nothing will change immediately until new laws are introduced.