The only problem with Oxford would be the average student has around 94% A* I'm pretty sure, a 0.94 proportion. With your GCSEs, though they are fantastic, this leaves you with only 77% so 0.77 which is under the average for an offer. It looks as though a few people got offers with 0.77 but it was a very small minority. Cambridge as you have already said like high UMS, although you still have 90% which is still a good result and you may still be in with a chance. I know Cambridge place a lot of emphasis on the BMAT so if you do take the risk of applying there make sure you have prepared. I personally found all the revision I did for it was useless, but if your school are offering some kind of help definitely take it.
I know Oxford and Cambridge are fantastic (I spent a week on the Oxford summer school and it was a lovely place), but there are many other fantastic universities that you would be able to make a very strong application too. Cardiff is one that will love your academics (they score based on your GCSEs and as long as your As weren't in English Language, Maths or the three sciences you would get full marks as it is out of your top 9 with an A*=3, A=2 and B=1 to give a score out of 27) and the course is fab. Another great one is Birmingham who like lots of A*s and they 'prefer' 4 As at AS Level so with 5 you would do very well. I'm pretty sure Leicester and Liverpool also look highly on GCSE grades.
It's a risk applying to either of them but if you do make sure you use it as your BMAT choice, or one other BMAT university as a maximum. It's a very difficult test and as you don't know your score until afterwards you don't want to risk getting rejections purely because of it when you have such good stats elsewhere.
Good luck!