Her whole family and their aristocratic social circle spoke like that, she grew up speaking like that. She's not putting it on, that's who she was. The growing pressure for royalty to be less aloof forced a gradual move to more "normal" speech from about the 70s. At the same time, broadcasters were starting to hire people with (gasp) regional accents. Previously anyone aspiring to be a newsreader etc had to speak RP, "the queen's English".