In the Netflix show “The Crown,” characters such as HM George VI, HM Elizabeth, their families and the Prime Minister often use the phrases “King of England” or “Queen of England” in casual conversation. Is that accurate, given the Act of Union (1707)? Is it reasonable to expect that these people would, in casual conversation, use that terminology rather than “King/Queen of the United Kingdom”?
Does the office of Queen of England even exist anymore?
The last Queen of England was Queen Anne (a Stuart monarch), who became the queen of Great Britain upon the Acts of Union in 1707 -- she had been queen of England, Scotland and Ireland separately before that time. The current queen, Elizabeth II of the house of Windsor, is often referred to as the queen of England, though that's not technically her title. She is queen separately of the various Commonwealth realms^1, but the UK is a single entity within her titles.
As for why she's referred to as the queen of England, it's a colloquialism that speaks to England's often leading role in the creation of the UK and British commonwealth -- England is often used as a shorthand for Britain in general, to the infinite annoyance of the other various constituent nations.
1: These are: Antigua and Barbuda, Australia, Barbados, Belize, Canada, Grenada, Jamaica, New Zealand, Papua New Guinea, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Solomon Islands, The Bahamas, Tuvalu, and the United Kingdom. n.b. I copied those from Wikipedia because I never can remember all of them at once.