I'm not a legal professional, but I would doubt the court would find in favour of the school unless there was something tangible to say you knew - e.g. previous flights & payment (by you) of charges into the same airport, you agreeing to some general exclusion ("blah blah charges are not included")... there has to be something that either explicitly or implicitly gets your consent.
Then again, you have to go to court, which is a bit dull. Esp. for 300 quid.
Best of luck.