There is a university choral society, but from what I gather, it's pretty much invitation-only, hand-picked from the college choirs. College choirs are of varying difficulty of entry - from impossible - especially if you're a girl (King's, John's) very very hard (Clare, Trinity), to more normal ones where it as actually possible to get in even if you weren't in National Youth Choir etc. College music societies are similarly variable.
There are two main university orchestras: CUSO (Cambridge University Symphony Orchestra) and the rather unfortunate CUMS (Cambridge University Music Society) which has two orchestras. CUMS 1 and CUSO are of similar standard (at least grade 8/diploma), CUMS 2 is slightly lower, but still around grade 8 for strings, probably more for wind/brass. There is also UCPO (University of Cambridge Philharmonic Orchestra) which is non-audition, of a reasonable quality but slightly unbalanced in favour of wind and brass (i.e. 25 flutes
). College music socs also have their own orchestras.