I reapplied to Oxford for maths and got rejected. My full grades are in my profile, but to sum them up, AAAAa at A-level (over 90% in maths and further maths) + Distinction in AEA Maths + 1,1 in STEP I and II.
I have spent many years obsessing over the Oxbridge admissions process - 4 admissions cycles of which 2 I spent at least 4 hours a day researching. Save yourself the trouble and listen to me. Oxford only cares about 2 things:
1) The admissions test - if you score over 90%, you're almost guaranteed an offer (think I heard a tutor say that no one's ever been rejected who's scored over 90). Otherwise, you need to be aiming for 75%.
2) The interviews - you need to get 2 good interviews out of 3 - 1 good, 1 ok and 1 bad usually doesn't cut it (which is what happened to me).
Oxford does take candidates who reapply, but not that many reapply. Certainly I think the admissions test should be a lot easier second time round, particularly if you've had practise with STEP. Should easily be getting 90%+ second time round. I ended up running out of time in my exam with only 10 mins left for 15% of the paper with the rest not even completed. I scored in the low 70s.
Good luck.