Cambridge doesn't care about GCSEs, Oxford does but it varies between courses how important they are (and good performance on the relevant pre-interview assessment will outweigh GCSEs usually). Otherwise the only one I know of that seems to scrutinise GCSEs in any way are some courses at LSE (mainly the very competitive ones), and some (but not all) medical schools which use them as part of their shortlisting criteria (including Oxford but not, as above, Cambridge).
By and large GCSEs won't make much difference provided you do well in A-levels.