I have 4 GCSEs and a level 2 Functional Skills in ICT. Maths (6), English (6), Business (5), Foundation statistics (5).
I done crap in my first set of A Levels - Geography (E), Economics (D) (Teacher predicted grades).
This past year I done a new set of A Levels independently and finished the exams a week ago - Maths, Further Maths and Computer Science. Predicted A* in all but Further maths was pretty hard this year. Got offers for CS from RHuL, QMuL, and City. I got rejected from KCL and UCL. My personal statement was good but I got rejected from KCL and UCL due to competitiveness, likely due to my GCSEs.
Just try your best and chose 2-3 High uni's like UCL or KCL and make the rest mid / safe and you should be fine. Bare in mind a lot of uni's require 5 minimum GCSE's, some of the ones I applied to like RHUL required it but I still got it, it just depends and contact them.