At Shuttleworth they arranged pairs of desks for the flight planning exam, at a student's request. However this was not standard, and that centre is no longer in use. You could try at Silsoe; probably not worth it at Gatwick!
CAA might be self-funded, but the exams have for years been a lot more expensive per hour than your lessons, and there you have a skilled instructor to each class of between 5 and 15 students (in most schools)! He has to prepare classes, which shold be more work than running the exam - you should not be charged for the incompetence of the JAA in setting up teh exams, giving exrta work marking. That is immoral and disgraceful, being charged extra due to the poor service you are receiving!