Most graduate careers do not require any specific discipline. English graduates go into advertising, investment banking, consultancy, the civil service, marketing, accounting, business, the law, the media, creative industries--basically any career that does not require specific scientific or economic expertise is possible.
Hiya! My name is Anja, I'm a Student Ambassador at the University of Reading and I studied English Lit and International Relations. The thing with English is that it teaches you lots of transferrable skills; communication, time management, self-motivation, independent thinking, creativity, research, and more. There are English specific careers (journalism, writing, publishing, editing, teaching, academia, librarian, etc.) as well as less directly connected ones (PR, third sector work, research, management, advertising, museum work, etc.) that are open to graduates. So there's lots more than just teaching Anja