The EU has been unaware of what GCHQ was doing until recently (Snowden). http://www.telegraph.co.uk/news/worldnews/europe/eu/10144217/EU-demands-answers-on-GCHQ-snooping.html And then they ruled it was likely illegal now that they've been investigating: https://www.theguardian.com/world/2014/jan/09/nsa-gchq-illegal-european-parliamentary-inquiry After Brexit? GCHQ doesn't care what the EU thinks anymore, and any legal action EU could have taken and seemingly wanted to take against GCHQ is gone. It's not about the intelligence agencies caring or not caring about breaking the law, it's the fact that they have now been publicly accused of breaking it only a couple of years ago by the EU. The EU works at the speed of tortoise, so nothing has been done about it yet but it was likely it would have. And of course, in the style of their actions against Microsoft and Google monopolies, they probably would have screwed it up by missing the point, but it would have still made GCHQ's job more complicated for sure and GCHQ definitely is partying this weekend whether it was their idea to start Brexit or not.