Visas are only required if you are studying outside of Europe, or if you are a non-EU student (to study or work within Europe). UK and EU citizens do not need visas to study within the EU or EEA (Norway, Iceland, Liechtenstein).
You're responsible for applying for a visa if you need one. It’s best to apply as soon as possible once your exchange place is confirmed. You can read about how to apply for a visa for going on exchange here: