Students get discounted rates on access to most sights in Great Britain. You need to have an International Student ID, available from a variety of sources. Whenever you purchase a ticket for admission to any sight, always ask if they offer a student rate.
Those under the age of 26 also receive steeply discounted rates on rail fare throughout the country, although not on London Transport. To receive the cheap fares you will need to get a Young Person's Railcard. To do that, you must go in person to a ticket office with your passport or International Student Card and a passport-size photo (there are photo machines in most large train stations). The youth railcard costs £20, but it can pay for itself in one train journey. Once you have it, show it at the ticket counter whenever you buy a train ticket in order to receive the discounted rates, and you'll also have to show it to the conductor on-board the train when he or she comes to check your ticket. Discount bus cards are also available for young people.