LONDON — Since Laurence Olivier became the first artistic director of the National Theater here, in 1963, its public image has been a blessing and a curse.

Officially named the Royal National Theater, it is the epitome of British high culture, favoring a Burke’s Peerage-like roster of artists — Shakespeare and Marlowe, Michael Frayn and Alan Bennett, John Gielgud and Helen Mirren — many of whom have been made knights and dames by the queen. The National’s three stages (and West End hits like “War Horse” and “One Man, Two Guvnors”) have never been more popular, with about 1.5 million theatergoers in London in the 2012-13 season compared with 817,000 four years earlier.

Put another way, this establishment appeal has made the National something like heaven for old fogies. While its leaders don’t have data on the average age of audience members, the National is hardly synonymous with “raw, rough, experimental theater” that can attract younger audiences who help ensure a future.

But “raw, rough, experimental theater” is now a stated mission at the Shed, the National’s red-timber cube of a building with chimney stacks rising from its four corners, visible above the tree line along the Thames.