To all those saying to go to Stanford, looking at this from a cost/benefit point of view:
The benefit of going to Stanford over Cambridge is basically negligible, there is no way you will be denied opportunities because you chose Cambridge over Stanford.
Considering the above, I truly believe that the additional fees for studying in the US as an international are not worth paying, when you have the opportunity to pay just £9000 a year and still go to a university just as good.
Education is an investment, and you should aim to get the best return possible. Cambridge will provide the best return in this case.