A combination of excellent A-levels, a high admissions test score (if your course has one) and very good interview performance could give you a good chance, particularly if you apply to Cambridge, which tends to put less weight on GCSEs than Oxford. Some courses do look at GCSEs more than others, but all will view them in context, so if you went to an "underperforming" school, then this would put you in a better position than if you went to a high performing (especially private) school where it was common for students to get 10+ A*s, unless you had other extenuating circumstances.