Personally, I would suggest emailing the relevant part of the University's Faculty of Mathematics, where you can find contact information on the bottom of the this page: <
I don't know how much you know about how the University of Cambridge operates, but if you were to apply for the one-year Masters, you would also need to look at the different colleges at Cambridge (there's more information available here: < The University also has open days (both generally and faculty specific) throughout the year, so it may be worth having a look to see when they are.
On a more personal note, I doubt your age would be a barrier to getting onto the Part III course, provided there is a satisfactory explanation as to why - my expeirence with the Faculty members (I'm an undergraduate studying Maths at Cambridge) is that they only really care for a person's mathematical ability.