If I were you, I would visit the websites of some of the bigger gaming companies, and see what they are looking for in their designers. You might be surprised.

From Blizzard’s website:

Game Designer and Level Designer

Game designers and level designers are often the most sought-after positions in a game company. Who wouldn’t want to be the guy who designs the heroes, villains, and dungeons? Game designers are the creative minds that help flesh out all the cool ideas into gaming reality. They are in charge of balance, storyline, and the background world. Like producers, game designers are rarely hired from outside the company, and if we do hire someone, that person would have extensive experience within the gaming industry. Often, the best chance of moving into a major game designer position would be to excel in level design.

Level designers are in charge of creating the actual game world–placing monsters, mountain ranges, and villages throughout the realm. A good applicant for level designer would send a demo CD containing 3D levels designed for another game, such as Quake or Half Life. Remember, the future of gaming is 3D, so please do not bother sending us old 2D maps of StarCraft or Warcraft II. Include a text file with your levels to give instructions on how to load the levels and to provide a brief summary of your thought processes that went into making the levels.

http://www.blizzard.com/jobopp/

Do your research before dropping 50K on a degree.

there are courses out there to do at university like im on one called computer games technology were we look at all aspecs of games creation. to get into the industry you have to work really hard and lots of people dont make it as its really competitive. Im on a placement year but failed to get a job in a games company because my demo disk was good enough. i have worked as a games tester for a few months and if you have a degree in computings or even if you dont, as long as you demo disk is amazing you have a chance. but remember you dont need to work for a company the people who make guitar hero werent a big company before they were just like bedroom designers and developers.