You can do a CCK (Certificate of Competent Knowledge) in another language in your “spare” time(!?!). But that’s not for learning a language from scratch, it’s just to practice and get a certificate in one you already know. You won’t have much spare time unless you are extremely competent in your primary language(s) already.
So my wife did German and Spanish (Spanish from scratch), but got a CCK in French, which she had done along with German at A-level.
Note also that the Cambridge course is very literature heavy. That may or may not be your thing, but there’s not much choice about it in the first two years. If you are doing Japanese from scratch that may be an intimidating prospect.