^
If threads about Imperial (for Maths) is anything to go by, then quite a few students/former students seem to attribute their dissatisfaction to poor tutorials, racial segregation (apparently, foreigners represent a majority, especially the Asians, who in general, have their own little cliques), not enough options in the 4th year, not much in the way of pure stats, no collaboration between the math and physics departments which leads to some weirdness if one takes the "Maths w/Mathematical Physics" option and there's probably a few other things but that's all I can remember off the top of my head.
If you have the money, then definitely give Cambridge a shot. Note that you should be doing Mathematics and Further Mathematics at A-Level, if you want to go down the math route. You should be looking at achieving at least A*AA. Accepted applicants sometimes have even better grades. A friend of mine was given a conditional offer of A*A*A but that was for English. However, such offers for all other courses aren't unheard of. Also, applying to specific colleges can have different implications, in that some won't mind if somebody is only doing Further Maths at AS-Level, while others wouldn't even consider you if you don't have it. Trinity is especially picky. If I recall correctly, colleges have varying interview processes. Sometimes, if a given college doesn't like you but they deem you as potential Cambridge material, you get "pooled" to another college.
There's two ways to do physics at Cambridge. One, is applying for the Mathematics degree and after Part IA, switching to Physics. The other is applying to Natural Sciences and taking the two (?) physics options and then switching to straight-up physics in the second year. (Part IB)
For the latter, you probably won't be "required" to do Further Maths. Remember that you will have to also write the STEP exam if you're applying for the Mathematics degree. To get an idea of how the interview process is, Google "Emmanuel College Mock Interviews".
The STEP exam consists of questions based on material you've covered in A-Level but they're much, much harder. Past papers are available on their website, I think. I should get down to doing a few of those myself. I'm not applying to Cambridge (too expensive for me and besides, I'm not willing to take a loan in the range of 30-40k pounds, assuming I could even get one) but a university I'm applying to has an entrance exam which is rather similar to STEP.