I would not worry at all, the advice I got from Cambridge, and Oxford, when I applied is that if you did not perform well at GCSE level (and mostly A grades is certainly not underperforming) they are not overly concerned.
Oxford and Cambridge tend to pay more attention to your AS grades, predictions, and how you did in any of the 'application papers' you have to sit for Law, History, Medicine etc. anyway. They accept that some people 'academically bloom' late and, although constant high academic performance is a good thing, they are more concerned with your performance when you apply and start the course than your performance at GCSE. As long as your GCSE grades are high enough and respectable, the door is not shut to Oxford or Cambridge! This is something that impressed me about their application process in general, where Durham and the LSE tend to just say ‘6 or 7 A*s or you do not get an offer’ it tends to let people in who may not have significantly shown the skills that are required for a degree.
There is a lot of debate over whether GCSEs are a good indicator of degree performance, but tbh, as qualifications they are nothing of the sort. Yes doing a wide range of topics can be a good test for degree level but looking back on my GCSEs I could just put a ton of statistics, facts, and have a very poor structure on an essay and still do very well. A-level tests both your skills of knowledge and deployment as well as your ability to write well. This is something, I believe, that makes A-level results more useful as an indicator of degree performance than GCSEs. Anyway, sorry for going off topic of Durham's seemingly ignorant and naive application process but I've known a few people this year get turned down due to GCSEs at Durham who were very good candidates!
My advice would be, if your GCSE results are not outstanding in terms of performance, that you should not write about how good they are in your personal statement or let your teachers brag about them in your reference. I heard a story from Cambridge where a reference included how they were really impressed with the candidate for achieving a string of A and B grades which didn't really go down very well.