Brexit has been presented in the United Kingdom as an opportunity to escape the Court of Justice of the European Union and EU law in general. However, the principle of legal certainty precludes EU law from losing all legal effect in the territory of UK in the very moment of withdrawal from EU. EU law will continue to bind individuals and confer rights on them at least for some time, albeit on different legal basis. Determining the scope of application of EU law after Brexit in the UK, is not only a matter for UK and EU negotiators to agree on a sensible arrangement of future relations, it is also a challenge for lawyers. The paper also briefly outlines possible scenarios of future involvement of the UK in economic structures on the European continent, and more specifically deals with the question of applicability of EU law in case United Kingdom becomes a member of the European Economic Area.