I am rather inclined to agree with Phlebas.
there are several points that you do need to consider.
(i) why cambridge in the first place?
Don't get me wrong, I really do think it is an outstanding place of study; for the right person
(ii) I have no idea about your level of ability, so this is not to put you off. Successful Math applicants are superb at maths. I don't mean that they simply get a grade A in Maths and Further Maths, I really mean that they have something very, very special in this discipline. I have taught the subject for many years, and in honesty, most of the students get an A grade, and indeed many go on to study at oxford or cambridge (mainly eng,phys,natsci); however the students who have successfully gained a place for mathematics have, without fail, been quite simply exceptional... students with a real PASSION for the subject, students who really go so far beyond the syllabus for no other reason than that they want to, Students who can teach me something, Students who I recognize as having an insight that cannot be taught. I run STEP tutorials, and can answer the questions because I have a degree in maths and a lot of practice, the students I tutor can answer STEP questions because they have raw ability.
(iii) most of the NAtsci/engineering students could have a fair stab at STEP too, but their real area of passion lies elsewhere. they are students who read way outside the mere bounds of the syllabus, and they do this because they genuinely want to, not to simply support an application.
so, the reality, oxbridge want the best, the academic elite. If you fit the bill then give it a shot.