I thought about it. They’d be useless.
You should probably look up King Juan Carlos of Spain, who thwarted a coup in the 1980s.
But the Queen has the ultimate power of being able to dissolve parliament - she’s the embodiment of the people. She also commands the forces, so if a government refused to budge, she could have them forcibly removed. In theory, she could also turn the forces on the people, but aside from being highly unlikely, I don’t think your average squaddie would be up for it!!!