You do have a King though. What would happen if the PM went to see him to form a government and they disagreed? The King is the one with armed guards, military rank and a fortress.
As part of his coronation, the King has sworn an oath to uphold the Law and to respect the primacy of Parliament. Not appointing the PM and his government has serious consequences as the PM is the leader of Parliament, which is the institution that has actually restored monarchy after the Glorious Revolution and which actually bankrolls the armed forces, and which was ultimately elected according to the Law by the citizens.
De facto means in fact. Given that the king does no governing no, he is not, in fact, the ruler. You may be looking for de jure, though I question even that.
The king of the UK still has to respect the Law. Being king does not mean that one can do as one pleased, or that there are no checks and balances. The last English king who tried to become an absolute ruler caused the English Civil War and was put on the chopping block by Parliament, as a matter of fact.
