Crown and Government

The Crown

The UK is governed in the name of the Queen, or the "Crown".  Halsbury's Laws of England states:
[T]he United Kingdom executive is formally referred to as Her Majesty's government; the law-making power of Parliament, of which the monarch is a constituent part, is described as being vested in the Queen-in-Parliament; and the judicial work of the higher courts is spoken of as being carried on by Her Majesty's judges.
In past times, British monarchs ruled as well as reigned, and even in the modern age some constitutional writers took a high view of royal authority.  However, there is a long tradition of seeing the monarch as acting within and subject to the law.  Henry of Bracton wrote in the 13th century:
But the King himself ought not to be subject to man, but subject to God and to the law, for the law makes the King.  Let the King, then, attribute to the law what the law attributes to him, namely dominion and power, for there is no king where the will and not the law has dominion.
Today, the role of the monarch is almost entirely formal and ceremonial.  The monarchy itself acknowledges that it "no longer has a political or executive role", though it is often said that the Queen retains the right to be consulted by, to encourage and to warn her ministers.

The reigning monarch of the UK is Queen Elizabeth II.  She is formally known as "Elizabeth II, by the Grace of God of the United Kingdom of Great Britain and Northern Ireland and of Her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith".

For formal purposes, the Queen generally acts through her Privy Council, which also functions as a court.  

The Government

In practice, executive authority is exercised by Her Majesty's Government, and principally by the 23-member Cabinet.  The Government and the Cabinet are headed by the Prime Minister, who conventionally also serves in the office of First Lord of the Treasury.  His powers have changed somewhat over the years.

The remnants of the monarch's unilateral powers (known as the "royal prerogative") are almost invariably exercised today by members of the Government.