Commander-in-chief of the British Armed Forces

The Commander-in-Chief of the British Armed Forces is a position vested in the British monarch, currently Queen Elizabeth II, who as Sovereign and head of state is the ``Head of the Armed Forces''. Long-standing constitutional convention, however, has vested de facto executive authority, by the exercise of Royal Prerogative powers, in the Prime Minister and the Secretary of State for Defence, and the Prime Minister (acting with the support of the Cabinet) makes the key decisions on the use of the armed forces. The Queen, however, remains the ``ultimate authority'' of the military, with officers and personnel swearing allegiance only to the monarch.

Question: is the british prime minister commander in chief
Answer: no