J.K. Rowling made a very obvious effort to keep the muggle world and the world of magic as separate as possible. What I am looking for here is a fic where they are less separated, specifically one where the stuck up old families of HP don't just act like nobles, they actually are Lords and Ladies or descended directly from them.
The scene that sparked this idea was Vernon spouting off about the freakishness of wizards and those who attend Hogwarts to a magical 'guest' only to have them point out that the Queen was a Hogwarts alumnus. Just the mental image of him trying to reconcile the concepts was amusing enough that I would like to see someone write it, but just having a stronger connection between the muggle and magical world than Harry sees in canon could be interesting. They just don't bother keeping in touch with the Prime Minister either because they know he won't stick around long enough to be worth the effort or because the magical community is just as old fashioned in this as they are in most things and see the Queen as the true ruler of England, with the Minister of Magic merely acting in her stead to deal with day to day issues.