If you're a seasoned traveller you'll know that video streaming licensing rights have always been locked to the country you're in, not the country you come from: available Netflix titles will vary based on whether you're in the US or France, for example, while other services such as Sky Go don't work at all once you go outside the UK border.
As of 1 April, that all changed. New EU legislation on the portability of online content services is now in effect, which means the likes of Netflix and Amazon Prime Video have to give subscribers the same package of movies and shows no matter where in Europe they happen to be.
Only paid subscription services are covered, however – free-to-air services have the choice of whether or not to follow the guidelines. For the time being the BBC has confirmed that the iPlayer apps won't work in other EU countries, but the corporation is working on it, so you might be able take iPlayer abroad in the future.
What happens post-Brexit?
As for what happens after the UK leaves the EU in March 2019, it's not clear at the moment – like almost everything else, it's still up in the air. The UK might be able to negotiate a deal to keep the agreement with the EU states, or it might not. According to the UK government at least, no decision has been reached.
Other services, like music and ebooks, are also covered by the deal, so your Spotify collection should say intact as you hop between countries in Europe. Providers also have the option to offer extra local content on top of the library you're entitled to at home, the European Commission says.
Your paid-for streaming services should now all be working in the rest of Europe, provided no teething problems are encountered – Now TV and Amazon confirmed to Wired that it was all systems go as far as they were concerned. Make the most of your new found travelling freedom though, because it might not be around for long.