The constitutional powers of the monarch
The Queen herself retains four key constitutional powers. Only the Queen herself may exercise these powers. No minister or advisor may exercise these powers on her behalf.
The power to appoint the Prime Minister
Legally, the Queen has the power to appoint whomever she wishes to be the Prime Minister. Equally, if she so decided, she could appoint nobody to the office and could keep it vacant. There is no legal requirement even that the person appointed as Prime Minister be a Member of Parliament. Conventionally, however, the Prime Minister is the leader of the party with an overall majority of seats in the House of Commons. As long as there is such a majority, and as long as the party concerned has a clear leader, the Queen will have no real choice. But these things are not always so clear.
In 1957, when the Conservative party was in office, it was not clear who should succeed Eden as leader of the party and Prime Minister. The Queen effectively chose Macmillan over Butler. In 1963, when Macmillan was too ill to continue, the Queen, in the words of her biographer, allowed herself to be 'duped by' Macmillan into once again ensuring that Butler did not become Prime Minister, inviting Sir Alec Douglas Home to form a Government. The Queen's biographer describes this as 'the biggest political misjudgement of her reign'. Finally, in 1974 when there was a Hung Parliament no one party commanded a majority of seats in the Commons. This time the party leaders acted wisely, effectively keeping the Queen out of it until it had become clear that Harold Wilson should be invited to form a minority administration. Shockingly, there is no guarantee that this would necessarily happen again.
The power to dissolve Parliament
A dissolution of Parliament is the device that triggers a General Election. Only the Queen can dissolve Parliament and she has the power so to act at any time, for any reason, or for none. Normally the Queen will dissolve Parliament only on the advice of the Prime Minister. But Edward VII insisted on a dissolution in 1910 before he would agree to act on certain policies preferred by the Prime Minister of the day (Asquith). A full constitutional crisis was prevented only by the King's death and his replacement by George V.
In 1974 Prime Minister Harold Wilson called a second election following a very narrow victory over his Conservative opponents a few months earlier. It has been made clear since that the Queen was under no obligation to grant this request for an election. The Queen had the power to tell Wilson that the people had only recently been asked to vote and that their decision should be respected, that it was up to him to find a way to make his minority government work. In the event she granted his wish and he was returned with a small majority.
In 1990, when Margaret Thatcher was going through her prolonged removal from office at the hands of her parliamentary colleagues, there were real fears that she would out-maneuver them by calling an election. The Queen would have been within her 'rights' to deny such a request on the grounds that it was self-serving, and not in the interests of the country.
The power to dismiss the Government
Legally, the Queen has the power to dismiss the Government at any time and for any reason or for none. No exercise of this power could be struck down by any court of law. This power was last exercised in the United Kingdom by William IV in 1834, but it remains in place. It was exercised with devastating effect in 1975 in Australia.
The power to withhold royal assent to legislation passed by the Houses of Parliament
No Bill can become a legally binding Act of Parliament unless and until it receives the royal assent. This means that the Queen has a veto on all legislation passed by Parliament. She has the power to withhold her assent to any legislation for any reason or for none. Were she to exercise this power no court could hold it illegal. This is an astonishing power. It was last exercised in the United Kingdom by Queen Anne in 1708 but has been threatened to be exercised several times in the twentieth century, not least, it is reported, by the current heir to the throne, Prince Charles.
The powers are very real
Even if some of these powers have not been exercised in the United Kingdom in many years, do not be fooled. Legally, they still exist. Several of them have been much more recently exercised by the Crown in Australia (where the Queen's appointed representative dismissed the democratically elected Government of the day in 1975) and in Canada (where the Queen's appointed representative prorogued Parliament for several weeks in late 2008, preventing it from performing its democratic and constitutional functions).