In the film, young Bess is mostly referred to as "Princess Elizabeth". In history, Elizabeth was denied that title from the age of three. Her father Henry VIII declared his marriage to Anne Boleyn invalid before her execution for treason, thus Elizabeth was declared illegitimate and only to be called "Lady Elizabeth".
The film shows Anne Boleyn lowering her head to the block to be executed as many traitors of that time were executed. Although the ax is not shown, the fact is that Anne Boleyn was executed in the "French style" - by a sword, kneeling with head erect, and not by an ax.
Early in the film, King Henry (Charles Laughton) is depicted as being very pleased with his toddler daughter. He reference to the young princess ads 'your future Queen Elizabeth'. In actuality, Henry's lifelong quest was for a son to succeed him. He divorced his first wife, Catherine of Aragon, because she wouldn't have a baby boy (in six tries, the only child that survived to adulthood was the future 'Bloody Mary') and he wasn't at all happy that the first child of his second wife, Anne Boleyn, was girl. If fact, the REAL reason Boleyn ended up being beheaded was because she wouldn't have a baby boy, either. Finally, wife three, Jane Seymour, had Edward, who succeed him. Then came Lady Jane Gray (only for nine days) then Mary, and finally Elizabeth.