A brief guide: The Crown and Executive Power
In the United States it is "the people" who prosecute criminals in the courts. In Britain it is "the crown." Thus we have the Crown Prosecution Service, rather than public prosecutors. It is "Her Majesty's Government." Cabinet ministers are her secretaries of state. In the United States the Senate approves the appointment of ambassadors. In Britain it is the queen who has that authority. Then there is "Her Majesty's Customs & Excise," and "Her Majesty's Inland Revenue" and so on.
These are, of course, government departments exercising the government's executive power. They are not controlled by the monarch However, the implication carried by these usages is that the executive branch properly gains its authority from above, not that it derives power from and is accountable to the people. The monarchy, not the people, is the symbolic source from which the British state takes its authority. And it is particularly difficult to hold the executive branch of government to account when power flows from the top (in Britain the Crown) downwards, rather than deriving from the people.
The Prime Minister is the chief beneficiary of executive privilege. More of the powers that the Prime Minister has come from her or his exercise of "crown prerogatives" than from any authority derived from a majority in the legislature. Anything that the government does without parliamentary consent takes whatever legitimacy it has from the prerogatives or rights of the crown. These "crown prerogatives" allow the government to declare war and sign treaties without the agreement of parliament. A more common sign of this privilege is the patronage that allows the Prime Minister to appoint senior judges, Anglican archbishops, the chiefs of staff and legislators-for-life.