Mona will be glad to hear that even in the UK, there is little formality these days:

There are also no obligatory codes of behaviour when meeting The Queen or a member of the Royal Family, but many people wish to observe the traditional forms. For men this is a neck bow (from the head only) whilst women do a small curtsy. Other people prefer simply to shake hands in the usual way.

Remember, the English once chopped off their King’s head, which goes a little beyond what happened in 1776.