It is folly to question the power of Queen Elizabeth. Any person whose name is a household word across the globe has an incredible amount of power based on that alone. Perhaps the monarchy does not have the sovereign and absolute power it once possessed but do not for one moment think that someone who can capture a headline on a whim or has personal ability to seek audience with any political leader in the country and perhaps even the world has run out of power.
England was once a monarchy, but has since changed its government form to a republic. England has historically been a monarchy state, but has changed in modern times. The Queen has no say in any legislation, or actions of the government. She is on government payroll, but is merely acting as a figure to portray the face of England. Although, she and the rest of the royal family are actively involved in politics, it is more so in an influential manner rather than actual power.