Well, that's what we are told.Charles will carry on being a thorn in peoples side, until he becomes King (if he ever does of course) and then he'll keep his views pretty much to himself. Cameron let slip that the Queen was pleased at the Brexit result, and she was not pleased that he'd let her private views become public knowledge. The Queen is just a figure head, nothing more. She doesn't have any say in the running of government, nor anything to do with the crown estates. She signs things put in front of her, and knows her place in the scheme of things.
I don't want to shock you too much, but the P.M. is a lady - like the Queen.As to weekly visits from the PM, I believe he updates her on the current state of things, but she's politically neutral, and just goes along with what Parliment suggests, even if she may express her view on things.
So, you think she (and her friends) have no influence at all. I just don't believe it.