Its natural, you tend to pick up the accent of the person teaching you. When I lived in Cuba, I had to laugh. I came home and there was a nice gentleman in the kitchen. He spoke English with a heavy English accent but he had some odd Jamaican slang thrown in. I found out he was my Cuban abuelo. He spent seven years living in Jamaica, so while he had picked up the phrases and slang of Jamaica, his accent came from the little British women who taught him.
Margrethe not only went to boarding school in England but later studied at Cambridge and London school of economics. Not only would majority of her teachers been British, but her fellow students as well.
Her mother may have been half English but she spoke Swedish around her daughter. I have read where she said that her Swedish was awful, visiting her cousins, until Benedikte was in the hospital and her nanny was with her. She spent more time with her mother then usual, and her Swedish improved.