Wait!

Before looking at further inspiration (from the sources below), make sure you check out My Supercurricular List! It'll give you a list of ideas on what was enough for me.

Supercurricular Insight

Have a look at Cambridge's Supercurricular List [local copy] for a start. These should give you a nice starting place to branch out from your chosen degree/course.

Oxford also has a nice collection of suggested resources which you can find here.

Following on from this, once you found a topic you're interested in, consider taking free courses from websites such as edx.org and MIT's open courses. Taking courses can be a great way of demonstrating development after gaining inspiration from the previous lists.

Supercurricular Action

While taking those courses serve as a bridge between Insight and Action, I find that the Action part is better suited for activities involving creation. For example, starting and leading a club or Writing for a Subject.

Other ideas for supercurricular action include creating a piece of software, building something, taking part in essay competitions or olympiads (ask your teacher), and getting work experience.