OK, I received an offer from Cambridge for Computer Science last month, so I hope my knowledge of the applications and interview process will be of some use.
Firstly, they don't expect you to know much about computing. The sum of my computing knowledge/experience at the time of the interview was:
Books/Articles:
Computer Science: An Overview, by Glenn Brookshear. Cannot recommend this enough, it's an amazing introduction and will give you a solid foundation in the subject. I picked up an old edition (about 2001) for £3 on Amazon, don't go spend £40 on the newest edition, there's no point, but it's a great way to show your interest.
Brian Hayes compsci articles in American Scientist: give a good perspective of applications in the real world, quite interesting. There are loads, but try to read a few.
Others:
Weeks work experience at a local software firm. Not sure how useful this actually was in the application, to be honest I didn't do much computing that week.
I did learn some Python in that week, so I mentioned that and some programs I'd written.
Extended project on cryptography (very much related to compsci). I genuinely believe this made the difference in my application, I'd certainly recommend it.
My point is, I had done VERY little computing prior to last summer, I'm sure you can fit in all of that stuff in the time you have left, and I was successful.
At the interview, they don't presume much knowledge of computing, this was the same for Imperial too. I spoke about cryptography for a bit, then did some problem solving questions (logic/maths puzzles). I didn't get any open ended questions like 'why do you want to study computer science', and I didn't really have to give any long answers.
Obviously, this is just my experience, and I can't promise it will be the same for all colleges, but the emphasis is VERY much on what you are capable of, they are aware computing is not widely taught, so they do not expect much prior knowledge, but the do expect you to have explored the field a bit to make sure it is what you want to do.
My offer is A*AA, with the A* in Maths. You seem capable of achieving this, so I wouldn't worry too much on those grounds.
So, best of luck, I'm sure you'll be fine, just READ