I am pretty sure there are no capital groups that you can get into up at Blackbushe. Its a bit of a drive but I would say the cheap flying would soon outweigh the petrol costs and membership fees that a club would charge. Not to mention the prohibitively expensive landing fees that BOH charges (it thinks it is the next LHR)!
Your going to be busy in class during the week which only leaves you free for weekend flying which invariably is the busiest time for clubs and hence aircraft availability will be at its lowest. Old Sarum might have some groups as well.