It would be a shock if more than 1 percent of the students at LSE have a car. It is this way for a number of reasons. First, cars are expensive to buy, maintain, and park; second, there is nowhere to park around campus or at most dormitories; and third, the public transportation in London is so good that it eliminates almost all need. In fact, one of the main advantages of going to school in a city like London is that cars are completely irrelevant.
If you want to get around town fast, then you should go the way of many students and get a bicycle. The biking culture in London is huge. There are many secondhand shops and secondhand websites where you can get a good bike for a great price. It is not risky to lock your bike up on the street, and on campus, as well as at every dormitory, there are "bike lots" where dozens of students lock up their bikes together. There are also bike lanes on most of the London streets, and the cars are all very used to driving with cyclists all around. It's good for the environment and cuts down the cost of your trip to campus!