Which of the following is categorized as an actual prerogative power?

Creating peerages is categorized as an actual prerogative power because it falls within the royal prerogative traditionally exercised by the monarch. This power allows the Crown to grant aristocratic titles to individuals, typically on the advice of the Prime Minister or other ministers. It represents a ceremonial function of the monarch, reflecting the historical powers that were once exercised by the sovereign without the need for parliamentary approval.

The other options involve different aspects of executive power, but they are either more complex or have evolved into roles with greater legislative oversight or political consensus. For example, declaring war often requires parliamentary approval or at least a debate within the House of Commons, and appointing ministers usually involves a more extensive process, including appointments by the Prime Minister that may need to be approved by Parliament. Appointing the Prime Minister, while a prerogative power of the monarch, is largely symbolic today; it is customary for the leader of the party that has won the most seats in a general election to be invited to form a government, thus making it a process heavily influenced by democratic principles rather than pure prerogative.