The UK should quickly tweak their royal succession laws, and give the crown to Edward, or Anne, while the queen is still alive.
If Charles abdicates, the line of succession dispute would be rather funny under the current succession laws.
If they too decline, line goes to their children below the age of majority, and the icky question of regency appears.
The regency in question notionally gives quite a lot of power, as the crown itself. If regency goes to the executive branch, it will throw out the last check on the Downing st. for may many thing, including the use of UK's nuclear weapons.
The monarchists were out in force, and downvoted your comment. I've upvoted it, but otherwise there's not much to do -- I think a lot of people who don't care for the monarchy probably avoiding the discussion.
I can sit and name persons more negatively treated for hours and not run out of names.
EDIT: Why is my comment collapsed? Genuine question, don't know how this works.