In short:
- You can vote
- You can be registered in one or both places
- You can vote in local elections in both places
- You can vote in national elections in one place only
Hopefully most of that is answered on this website:
Electoral Commission - Who Can Vote - Students
Hope that helps you - and if you can, do vote, and encourage others to do so too.
[Edit/rant] Also worth noting, as mentioned in the other reply - The Tories have brought in new rules to mean you must own and take photographic ID with you to be allowed to vote i.e. a passport or driving licence. If you're not wealthy enough to drive or have international holidays, you're no longer allowed to participate in democracy.