I did Physics, Maths and Design Technology (the one with making stuff, electronics, design, etc if it still exists). Back in maaaaaaaaaaar day that was a standard pick for getting into engineering but is pretty good/general for leaving doors open. Sounds like you might have some interest/creativity/artistic streak if you were considering art, and indeed you are planning to go into design, albeit games design, so Design Tech might be a complimentary course, its pretty easy/fun, and ought to be regarded better than art for the sort of thing you want to get into eventually.
I did indeed go into engineering. I dunno about all this alleged difficulty in engineering grads finding jobs - I can only imagine there are a lot of crap engineering grads with thirds from Mickey Mouse institutions who are the ones struggling, because we are literally crying out for engineers in the oil/gas industry at the moment. If you're good you'll get employed easily, and there's plenty of pay in this industry too.
If you're really set on the computing side, further maths would be good as said many times. You might consider going to your head and making an appeal for yourself if you havent already. You seem to have the grades so if you show a real enthusiasm you might get the opportunity. Seems a bit crap to be honest they are not actively encouraging you??