Aside from the extremely privileged local Harrow school kids, the area is actually very ethnically mixed. You'll find plenty of multicultural communities.
The Grim's Dyke Hotel, former home of W.S. Gilbert (of Gilbert & Sullivan fame) is in Harrow and holds regular Opera Dinners throughout the year.
Harrow School, although frighteningly posh, was in fact involved in the writing of the rules of Association Football. Churchill went there too.
Suburban and ethnically diverse, living in certain parts of Harrow can be purely for the elite, but mostly it is an incredibly culturally fascinating place.