Does the royal family of Britain have any actual political power?
In the normal course of events, the monarch has plenty of influence but little actual power. However, in times of constitutional crisis, the monarch has significant power. The most likely scenario (it has happened before and will probably happen again) is that there is a “hung parliament” i.e. there has been an election but no one party has an absolute majority. The monarch has the power to decide whether to ask one of the party leaders to form a minority administration or to call another general election.