In the British monarchy, there is no one person who holds the supreme power. Instead, the supreme power rests in the Parliament. Today, that effectively means that the House of Commons has the supreme power.
The monarch in the British system has no real power. She technically holds supreme executive (but not legislative) power, but does not use it in practice. Instead, Parliament has the real power. It is Parliament that makes the laws. The members of the cabinet, who oversee the executive branch, are all members of Parliament and are responsible to Parliament. Thus, Parliament holds supreme power.