The show seems to suggest that the cabinet should be consulted for things like what the royal children should be called and whether members of the royal family can fly airplanes (I'm only on episode four, so there are probably more examples in the show).
This is interesting to me. Was it always like that or how did that kind of relationship develop overtime? Were some prime ministers more interested in directing the affairs of the royal family over others?
To add on to your question, were there any British PM's who harbored any sort of personal resentment or disdain for the Royal family? I know that some PM's in other Commonwealth realms did but what is the history of that in the UK?