JAR and later EASA were established primarily to support CAT across the EU and a few neighbouring states who wanted to join the party. The goal was to ensure that, for example, a pilot with a German ATPL living in Austria could fly a French registered aircraft from Budapest to London with the minimum of paperwork. GA got swept up in all this by people who didn’t really understand it. Much lobbying and EASA hiring a number of people who hold and use PPLs has started the process of rowing back to situation rather better than Pre-EASA in many states. Though some NAAs are more helpful in this than others.
Brexit needs to either remain with it by agreement or find a way to replace it all, which won’t be easy or quick.