Haha, yes, I thought the same too when I opened the handbook. I agree with you, some kind of predatory animal would be much better! However I did manage to find the explanation somewhere on the Student Union website:
"In the formative days of the Union, sports clubs travelled to and from the sports grounds at Palmers Green using a horse-drawn bus. Because of the frequent reluctance of the horse to cooperate a carrot was often dangled in front of its nose. This became such a regular occurrence that the carrot found itself a mascot of the Union. It was first called “His Most Noble Majesty, King Carrot”. Various versions of the carrot have existed, from fibreglass to cloth. Alarms were set up to alert students in case of Mascot Raids by other London Student Unions – everybody would rush out of lectures to save the carrot from its foes! Consequently, the Union mascot during the 1970s was made out of 4 tonnes of concrete attached by steel bands to a pillar in the bar, called reverently by the name of King Carrot VI.
After a short sabbatical, when it was taking a well earned break, the carrot has returned home and assumed its rightful position of the ultimate in cool, style, image and prominence (Yeah!). When you see the Carrot you can be guaranteed a good time. The Carrot represents the lighter side of life at City. Sports, music, dancing and generally having a good time."