In theory yes, whether you can do it through your school or if you have to do it privately may vary. At my school I did know people who resat GCSE Maths in year 12, for example, and was vaguely aware the same thing was offered for English Language (although I didn't know anyone personally that had to resit English).
I'd suggest discussing it with your school. It would probably be better to try and resit it in year 12, rather than year 13, so you don't have it on top of your A-level exams, if at all possible.