Humphrey Hughes (Alex Jennings) is pictured with Prince Charles (later King Charles III) in a photograph. Jennings portrayed Charles in La reina (2006).
When Hayley learns James is technically a Royal, he says he is 307th in line to the throne, so a lot of people would have to die before he appeared in The Crown (2016). Both Alex Jennings (Humphrey) and Harriet Walter (Iris) appeared on the show, as Edward VIII and Clementine Churchill respectively.
It appears that Lord Humphrey's title, Earl of Gloucester, is a courtesy title. When introducing his father, Lord Humphrey refers to him as "His Grace" indicating his father is a Duke. The son and heir apparent of a duke, marquess, or earl is permitted to use a title held by his father as long as it is a lower grade title than the one used by his father.
During their first telephone call, James tells Hayley that his father is the Earl of Gloucester. Later, while arguing during another call, she says to him "You are an Earl." This is not correct. James is in line for an earldom as his father's apparent only son. He would not be an earl as long as his father is alive and using the title.