Original: Quoted in Brandreth, pp. 105 - 106 Heiress presumptive As a granddaughter of the monarch in the male line, Elizabeth held the title of a British princess, with the style Her Royal Highness, her full style being Her Royal Highness Princess Elizabeth of York.
Simplified: As a granddaughter of the British sovereign (king), the princess was called "Her Royal Highness Princess Elizabeth of York".