I finished my BCL examinations yesterday! As for dress for exams, BCL candidates do not have a different academic dress to other graduate students. You will wear sub-fusc with the advanced student’s gown: it's rather like the commoner’s gown but longer. You may as an alternative choose to wear the academic dress of your prior University with sub-fusc, so a Hull gown would be permissible. I wore my Cambridge B.A. gown and hood rather than my Oxford degree, some other ‘Tabs did likewise. In addition most people will wear a carnation- a white one for the first exam, pink for the middle ones, and red for the final. Sub-fusc for a female consists of a white shirt, black skirt, tights, black shoes and ribbon (you also carry a mortarboard); far cooler than the male equivalent which requires a jacket and white bow tie. Before you worry about overheating you need only wear the attire entering and exiting the exam hall- it is permissible to remove ones jacket and gown during the examination.
It may seem somewhat old fashioned, but it is a remarkably good tradition. Dressing up for the examination helps to psyche up the mind; and it certainly helps makes the day of finishing a momentous occasion, with the ceremonial trashing and photo shoots.