Sherborne School

(Looks a bit like Hogwarts, eh?)

Founded in 1550, Sherborne is an independent school for boys ages 13-18 with heavy tradition that provides "An invigorating, intellectually sound and multi-faceted environment'' though it's also been described as "not always gentle." Sherborne has many notable alums in fields ranging from acting (Jeremy Irons) and academia (Turing and Alfred Whitehead) to international royalty. Though it used to concentrate heavily on the classics--like most British boys schools of the era.
Modern students dress as such on a daily basis.
Uniforms from the late 1960s--ah, the boaters...
Turing at Sherborne. He was considered "antisocial" and his work "messy" as a student. He seemed to focus on investigation beyond his level of mathematics rather than consolidating the basics. More accounts/details here .