does the queen of england appoint the prime minister
The monarch and his or her immediate family undertake various official, ceremonial, diplomatic and representational duties. As the monarchy is constitutional, the monarch is limited to non-partisan functions such as bestowing honours and appointing the Prime Minister. The monarch is commander-in-chief of the British Armed Forces. Though the ultimate formal executive authority over the government of the United Kingdom is still by and through the monarch's royal prerogative, these powers may only be used according to laws enacted in Parliament and, in practice, within the constraints of convention and precedent.
Monarchy of the United Kingdom