Nope; the Parliament makes the rules about succession. The order is established according to bloodline, and if there were to be changes, it would require an act of Parliament.
The Royal Family does not "rule" the UK. Their function in modern times is diplomatic, in many regards like our State Department and Ambassadors, and also cultural, as patrons of many arts, industries and charities, and in honorary leadership of many orders of the military. The Sovereign is also the head of the Church of England in much the same way that our President is Commander-in-Chief of our military; no one expects our President to get into the trenches; and their headship of the CoE is likewise a consultant relationship.
I am currently reading Dickens’ “A Child’s History of England” and find it very interesting!
Succession was handled mostly via sword and executioner’s axe back in the day.
The ‘old ways’ are more entertaining..................