I’m sure that you are all already more engaged in super-curricular activities than you realise. As Music students at Cambridge, you will be the unique position of having your pastime also be your academic interest. While you are not obliged to perform on an instrument as part of your degree course (other than Practical Musicianship in the first year), you’ll also probably find that there is an expectation for you to be involved in performances of various sorts.
It is also helpful to think about how music interacts with other disciplines, and try to find examples. For instance, if you decided to focus on music as depicted in art or architecture, you might visit the National Gallery and look at the way instruments and musicians are depicted through time. Or, if you have philosophical interests, be curious as to the terms and ways in which philosophers discuss music.
Go to as many concerts as you can! For example, consider going to some of the BBC Proms over the summer months.