Chris, do you mind me asking what grades you got at AS level and what you're predicted for A2 level? If you get the grades to go to a better uni then you might as well do that. I wouldn't see the point of taking a course for which you are overqualified.
The lack of any maths or science A level might be a problem, but your GCSEs are quite impressive, as is the number of A levels you are taking, especially since you didn't mention the abominable General Studies. The comp sci course I did just had an extra maths module for people who hadn't got at least a C in A level maths, to bring them up to the necessary level.
It occurs to me to ask whether you're sure you want to do programming. Taking those A levels as an indication of your favourite subjects, you might be more suited to a games design role, which has very little to do with programming. Not sure what degree course would be best for that, though.
If you do want to do programming, then I agree with the others who said to go for a straight computer science or software engineering course rather than games programming. I don't think a games programming course would teach you anything useful in addition to what you would learn on one of those other courses. That's what I did and when I interviewed for my first job the guy (who was lead programmer at this games company) said I made the right choice. Actually I didn't even complete my degree, but I impressed him with my knowledge of C and algorithms.
And finally: