My parents and teachers warned me as well about damage to my ego from being a "small fish" and although I'm sure there's something to what they're saying, I'm confident enough to suspect I have at least a chance of being at the top when I arrive at Oxford if I put forth my absolute best effort. I see it as a better attitude to take than the attitude of it being absolutely impossible to reach the top, and if I have my ego checked by failure, I'll at least have better marks and more of an education than if I coasted by thinking "average" was the best I could do.
At the end of the day, someone has to be the best. It's true, the people who are "only" average at Oxbridge performed just as well as any of the entering applicants, but the very top students at Oxbridge were also applicants indistinguishable from the others. To steal a phrase from my favorite Presidential candidate, I have the "Audacity to Hope."