Which role is NOT a prerogative power of the Prime Minister?

Appointing Supreme Court judges is indeed not a prerogative power of the Prime Minister. In the UK, the appointment of Supreme Court judges is carried out through a process that involves the Judicial Appointments Commission, which assesses candidates independently. Although the Prime Minister may have some influence in the appointment by making recommendations, the decision ultimately rests on a structured process that prioritizes judicial independence.

In contrast, the other roles mentioned—appointing ministers, declaring war and peace, and summoning Parliament—are recognized as prerogative powers where the Prime Minister has considerable authority. The ability to appoint ministers is a fundamental aspect of the Prime Minister's role, allowing them to choose members of the Cabinet and influence the government’s direction. Similarly, the power to declare war or make peace is traditionally at the disposal of the Prime Minister, reflecting the country's executive and military responsibilities. Summoning Parliament is also under the Prime Minister's control, as they manage the legislative timetable and the session's commencement.

Understanding these distinctions is critical for grasping the constitutional framework and the balance of powers within the UK government.