In a university like LSE, where academic excellence is prized above all else, drugs do not play a significant role in campus life. This does not mean that a drug scene does not exist, but it certainly does not dominate social life in the slightest. There is, therefore, absolutely no pressure to ever do drugs if you are not inclined to partake.
Drinking is a different story, on the other hand. You would be hard-pressed to find a student that does not drink at all—it is simply the culture of England and of most college-aged kids around the world. Drinking, for the most part, consists of a few beers after class with your friends and rarely goes until all hours of the night. Also, disciplinary action rarely has to be taken on the school's part because most students are over the drinking age (which is 18 in the United Kingdom), and most of the drinking is done off campus anyway. Without getting too political, the lower drinking age in England really seems to work, at least on a college campus. The school does not have to spend any time or effort regulating the drinking, and students do not have to get punished for something that every college student does anyway.