Mandatory reading
There is one book that all students should have read from cover to cover before starting the course:
Goldschlager, L. & Lister, A. (1988). Computer Science - a
Modern Introduction. Prentice-Hall (2nd ed.).
You should also try some of the exercises. In particular, the first 15 exercises at the end of Chapter 2 on the design of algorithms and the first 10 exercises at the end of Chapter 4 on computer architecture are relevant preparation for the introductory lecture courses.
Academic study of Computer Science relies on mathematical techniques
to formulate and analyse problems. An elegantly written presentation
of practical applications (some of them specifically related to
programming computers) is:
Körner, T. (1996). The Pleasures of Counting. Cambridge
University Press.
It will also help to pursue recreational mathematics in the form of games and puzzles to keep your skills tuned. Indeed, the exercises in Körner's book probably count as recreational mathematics.
General reading
After the technical reading suggested above, the next most important preparation is to build up a broad background understanding of current issues in Computer Science. An excellent informal collection of accessible and relevant articles can be found in:
Dewdney, A.K. (1993). The New Turing Omnibus. Computer Science Press.
A classic study which remains completely relevant is:
Brooks, F.P. (1995). The Mythical Man Month (Anniversary
edition). Addison-Wesley.
Byte and magazines like New Scientist and Scientific American often have relevant articles; popular computing magazines tend to have a commercial emphasis which is less useful. The April 1995 issue of Scientific American had a set of particularly interesting articles on The Computer in the 21st Century.
Study skills
Learning at university is rather different from being taught at school. You will have to manage your own studies, scheduling your time and arranging classes. The Open University has produced an excellent book for its students which includes much that is directly relevant to more conventional universities and will continue to be valuable throughout your time in Cambridge:
Northedge, A., Thomas, J., Lane, A. & Peasgood, A. (1997). The
Sciences Good Study Guide. Open University.
Course reading
You might like to look at some of the text books that are listed elsewhere in this document. Printed notes will be handed out for most courses, so you don't actually need to buy all of the books.
http://www.cl.cam.ac.uk/UoCCL/teaching/preparation.html gives some more information about preparation for the course.