The first thing you need to resolve, in your mind, is what you mean by "occassional gaming". That is what will determine what laptop you need, and what you need to spend. MOST modern laptops will handle the rest of your wish list. You can virtually pick what RAM and hard drive you want, at a price.
Whatever laptop you choose, if you want to protect your uni work, budget for a portable hard drive, say 500GB at around £70 ( or £150 for a good 1TB desktop hard drive, if you can afford it), to back up what you can't afford to loose.
In terms of manufacturers: Dell, Asus, and Acer all do good performance laptops. If you give some idea of the sort of games you are hoping to play, I'm sure someone can give more detailed advice.