Lycaon pictus is right. Charlotte indeed was already married with man who would be first king of Belgium in OTL. So this would mean that the country will has different ruling house if exists.
In UK not necessarility dramatic changes. Monarch wasn't anymore so all-powerful person. There is probably some cultural affects anyway.
Well, considering she would probably be not that powerful and the fact that she would presumably only succeed less than two months before the Belgian revolt, there's little chance her coming to the throne would butterfly away Belgium, I guess. Unless she would be diplomatically much more meddling than her successors AND get really fast at learning the political game. Scanning her bio on wikipedia (yes, I admit!), she does seem to have been able to "play politics" in order not to marry the Prince of Orange, but nothing really suggests that she would do it for something outside her personal interest. OTOH, a princess at the age of twenty might act differently than a queen at the age of 35 ... Her husband did have a confirmed interest in political meddling, though, so I could eventually see him try to play some political role, possibly creating some form of controversy or constitutional crisis.
But yes: hurray for having no Leopold II in Congo!