London is a long way, but i agree, to come to England and not visit London would be a bit of a disappointment for you.
Id advice you visit London, but if your in a bar or a cafe, just ask the locals,they are quite friendly, and some just talk for hours! They will be able to give you an idea of good thinks to do around the area! Im sure your educational campus will have a student services, where you could explain you want to visit as many places as possible in England while attending education, and they will give you information!