does the prime minister have the power to declare war
A declaration of war is a formal declaration issued by a national government indicating that a state of war exists between that nation and another. In the United Kingdom, only the monarch has the power to declare war and peace, under the royal prerogative. There have been no declarations of war since the Second World War, though British Armed Forces have taken part in armed conflict on numerous occasions nonetheless.
Declarations of war by Great Britain and the United Kingdom