Well they do depending on which country they are citizen of and where they are working.

The UK is considered non-EU so there would need to be a visa for a Brit working in the EU.

A nitpick here, but "visa" gets tossed around a lot. A visa is a document which allows you to request permission to enter a country for some purpose. To work in a country you need a work and/or residency permit. Even in the US, there are situations where you can work with a an expired visa, provided your other immigration documents are current. But if you leave, you need a new one. Similarly UK citizens can still work in some European countries without a visa, because there is no requirement for them to enter with one (but the officer at the border might still refuse entry).

Since the word used was "returning", that would mean that they go back to where they came from, where they are citizens.